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

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

Solve for w

$$w=-\frac{5s\left(2s+1\right)}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

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

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

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

Multiply 4 and 2 to get 8.

$$20s^{2}=\left(3s-3w-8s\right)\times 2$$

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

$$20s^{2}=\left(-5s-3w\right)\times 2$$

Use the distributive property to multiply -5s-3w by 2.

$$20s^{2}=-10s-6w$$

Swap sides so that all variable terms are on the left hand side.

$$-10s-6w=20s^{2}$$

Add 10s to both sides.

$$-6w=20s^{2}+10s$$

Divide both sides by -6.

$$\frac{-6w}{-6}=\frac{10s\left(2s+1\right)}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$w=\frac{10s\left(2s+1\right)}{-6}$$

Divide 10s\left(1+2s\right) by -6.

$$w=-\frac{5s\left(2s+1\right)}{3}$$

Solve for s (complex solution)

$$s=\frac{\sqrt{25-120w}}{20}-\frac{1}{4}$$

$$s=-\frac{\sqrt{25-120w}}{20}-\frac{1}{4}$$

Solve for s

$$s=\frac{\sqrt{25-120w}}{20}-\frac{1}{4}$$

$$s=-\frac{\sqrt{25-120w}}{20}-\frac{1}{4}\text{, }w\leq \frac{5}{24}$$