Solve (2x+7):3x=5:4=

$$( 2 x + 7 ) : 3 x = 5 : 4 =$$

Solve for x

$$x=\frac{\sqrt{79}-7}{4}\approx 0.472048604$$

$$x=\frac{-\sqrt{79}-7}{4}\approx -3.972048604$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4\left(2x+7\right)x=15$$

Use the distributive property to multiply 4 by 2x+7.

$$\left(8x+28\right)x=15$$

Use the distributive property to multiply 8x+28 by x.

$$8x^{2}+28x=15$$

Subtract 15 from both sides.

$$8x^{2}+28x-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 28 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-28±\sqrt{28^{2}-4\times 8\left(-15\right)}}{2\times 8}$$

Square 28.

$$x=\frac{-28±\sqrt{784-4\times 8\left(-15\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-28±\sqrt{784-32\left(-15\right)}}{2\times 8}$$

Multiply -32 times -15.

$$x=\frac{-28±\sqrt{784+480}}{2\times 8}$$

Add 784 to 480.

$$x=\frac{-28±\sqrt{1264}}{2\times 8}$$

Take the square root of 1264.

$$x=\frac{-28±4\sqrt{79}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-28±4\sqrt{79}}{16}$$

Now solve the equation x=\frac{-28±4\sqrt{79}}{16} when ± is plus. Add -28 to 4\sqrt{79}.

$$x=\frac{4\sqrt{79}-28}{16}$$

Divide -28+4\sqrt{79} by 16.

$$x=\frac{\sqrt{79}-7}{4}$$

Now solve the equation x=\frac{-28±4\sqrt{79}}{16} when ± is minus. Subtract 4\sqrt{79} from -28.

$$x=\frac{-4\sqrt{79}-28}{16}$$

Divide -28-4\sqrt{79} by 16.

$$x=\frac{-\sqrt{79}-7}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{79}-7}{4} x=\frac{-\sqrt{79}-7}{4}$$

Steps for Completing the Square

Multiply both sides of the equation by 12, the least common multiple of 3,4.

$$4\left(2x+7\right)x=15$$

Use the distributive property to multiply 4 by 2x+7.

$$\left(8x+28\right)x=15$$

Use the distributive property to multiply 8x+28 by x.

$$8x^{2}+28x=15$$

Divide both sides by 8.

$$\frac{8x^{2}+28x}{8}=\frac{15}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}+\frac{28}{8}x=\frac{15}{8}$$

Reduce the fraction \frac{28}{8} to lowest terms by extracting and canceling out 4.

$$x^{2}+\frac{7}{2}x=\frac{15}{8}$$

Divide \frac{7}{2}, the coefficient of the x term, by 2 to get \frac{7}{4}. Then add the square of \frac{7}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{7}{2}x+\left(\frac{7}{4}\right)^{2}=\frac{15}{8}+\left(\frac{7}{4}\right)^{2}$$

Square \frac{7}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{7}{2}x+\frac{49}{16}=\frac{15}{8}+\frac{49}{16}$$

Add \frac{15}{8} to \frac{49}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{7}{2}x+\frac{49}{16}=\frac{79}{16}$$

Factor x^{2}+\frac{7}{2}x+\frac{49}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{7}{4}\right)^{2}=\frac{79}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{7}{4}\right)^{2}}=\sqrt{\frac{79}{16}}$$

Simplify.

$$x+\frac{7}{4}=\frac{\sqrt{79}}{4} x+\frac{7}{4}=-\frac{\sqrt{79}}{4}$$

Subtract \frac{7}{4} from both sides of the equation.

$$x=\frac{\sqrt{79}-7}{4} x=\frac{-\sqrt{79}-7}{4}$$