Solve 4s^2=(3(s-1)-4(2s)/5)

$$4 s ^ { 2 } = ( \frac { 3 ( s - 1 ) - 4 ( 2 s ) } { 5 } )$$

Solve for s

$$s=\frac{\sqrt{215}i}{40}-\frac{1}{8}\approx -0.125+0.366571957i$$

$$s=-\frac{\sqrt{215}i}{40}-\frac{1}{8}\approx -0.125-0.366571957i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 5.

$$20s^{2}=3\left(s-1\right)-4\times 2s$$

Use the distributive property to multiply 3 by s-1.

$$20s^{2}=3s-3-4\times 2s$$

Multiply 4 and 2 to get 8.

$$20s^{2}=3s-3-8s$$

Combine 3s and -8s to get -5s.

$$20s^{2}=-5s-3$$

Add 5s to both sides.

$$20s^{2}+5s=-3$$

Add 3 to both sides.

$$20s^{2}+5s+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 5 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-5±\sqrt{5^{2}-4\times 20\times 3}}{2\times 20}$$

Square 5.

$$s=\frac{-5±\sqrt{25-4\times 20\times 3}}{2\times 20}$$

Multiply -4 times 20.

$$s=\frac{-5±\sqrt{25-80\times 3}}{2\times 20}$$

Multiply -80 times 3.

$$s=\frac{-5±\sqrt{25-240}}{2\times 20}$$

Add 25 to -240.

$$s=\frac{-5±\sqrt{-215}}{2\times 20}$$

Take the square root of -215.

$$s=\frac{-5±\sqrt{215}i}{2\times 20}$$

Multiply 2 times 20.

$$s=\frac{-5±\sqrt{215}i}{40}$$

Now solve the equation s=\frac{-5±\sqrt{215}i}{40} when ± is plus. Add -5 to i\sqrt{215}.

$$s=\frac{-5+\sqrt{215}i}{40}$$

Divide -5+i\sqrt{215} by 40.

$$s=\frac{\sqrt{215}i}{40}-\frac{1}{8}$$

Now solve the equation s=\frac{-5±\sqrt{215}i}{40} when ± is minus. Subtract i\sqrt{215} from -5.

$$s=\frac{-\sqrt{215}i-5}{40}$$

Divide -5-i\sqrt{215} by 40.

$$s=-\frac{\sqrt{215}i}{40}-\frac{1}{8}$$

The equation is now solved.

$$s=\frac{\sqrt{215}i}{40}-\frac{1}{8} s=-\frac{\sqrt{215}i}{40}-\frac{1}{8}$$

Steps for Completing the Square

Multiply both sides of the equation by 5.

$$20s^{2}=3\left(s-1\right)-4\times 2s$$

Use the distributive property to multiply 3 by s-1.

$$20s^{2}=3s-3-4\times 2s$$

Multiply 4 and 2 to get 8.

$$20s^{2}=3s-3-8s$$

Combine 3s and -8s to get -5s.

$$20s^{2}=-5s-3$$

Add 5s to both sides.

$$20s^{2}+5s=-3$$

Divide both sides by 20.

$$\frac{20s^{2}+5s}{20}=-\frac{3}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$s^{2}+\frac{5}{20}s=-\frac{3}{20}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$s^{2}+\frac{1}{4}s=-\frac{3}{20}$$

Divide \frac{1}{4}, the coefficient of the x term, by 2 to get \frac{1}{8}. Then add the square of \frac{1}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$s^{2}+\frac{1}{4}s+\left(\frac{1}{8}\right)^{2}=-\frac{3}{20}+\left(\frac{1}{8}\right)^{2}$$

Square \frac{1}{8} by squaring both the numerator and the denominator of the fraction.

$$s^{2}+\frac{1}{4}s+\frac{1}{64}=-\frac{3}{20}+\frac{1}{64}$$

Add -\frac{3}{20} to \frac{1}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$s^{2}+\frac{1}{4}s+\frac{1}{64}=-\frac{43}{320}$$

Factor s^{2}+\frac{1}{4}s+\frac{1}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(s+\frac{1}{8}\right)^{2}=-\frac{43}{320}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(s+\frac{1}{8}\right)^{2}}=\sqrt{-\frac{43}{320}}$$

Simplify.

$$s+\frac{1}{8}=\frac{\sqrt{215}i}{40} s+\frac{1}{8}=-\frac{\sqrt{215}i}{40}$$

Subtract \frac{1}{8} from both sides of the equation.

$$s=\frac{\sqrt{215}i}{40}-\frac{1}{8} s=-\frac{\sqrt{215}i}{40}-\frac{1}{8}$$