Solve x=(5x+7)(3x-4)

$$x = ( 5 x + 7 ) ( 3 x - 4 )$$

Solve for x

$$x = \frac{2 \sqrt{105}}{15} \approx 1.366260102$$

$$x = -\frac{2 \sqrt{105}}{15} \approx -1.366260102$$

Steps by Finding Square Root

Use the distributive property to multiply 5x+7 by 3x-4 and combine like terms.

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

Subtract 15x^{2} from both sides.

$$x-15x^{2}=x-28$$

Subtract x from both sides.

$$x-15x^{2}-x=-28$$

Combine x and -x to get 0.

$$-15x^{2}=-28$$

Divide both sides by -15.

$$x^{2}=\frac{-28}{-15}$$

Fraction \frac{-28}{-15} can be simplified to \frac{28}{15} by removing the negative sign from both the numerator and the denominator.

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

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{105}}{15} x=-\frac{2\sqrt{105}}{15}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5x+7 by 3x-4 and combine like terms.

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

Subtract 15x^{2} from both sides.

$$x-15x^{2}=x-28$$

Subtract x from both sides.

$$x-15x^{2}-x=-28$$

Combine x and -x to get 0.

$$-15x^{2}=-28$$

Add 28 to both sides.

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

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 28}}{2\left(-15\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 28}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60\times 28}}{2\left(-15\right)}$$

Multiply 60 times 28.

$$x=\frac{0±\sqrt{1680}}{2\left(-15\right)}$$

Take the square root of 1680.

$$x=\frac{0±4\sqrt{105}}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{0±4\sqrt{105}}{-30}$$

Now solve the equation x=\frac{0±4\sqrt{105}}{-30} when ± is plus.

$$x=-\frac{2\sqrt{105}}{15}$$

Now solve the equation x=\frac{0±4\sqrt{105}}{-30} when ± is minus.

$$x=\frac{2\sqrt{105}}{15}$$

The equation is now solved.

$$x=-\frac{2\sqrt{105}}{15} x=\frac{2\sqrt{105}}{15}$$