Solve (2x-3)^2=5x+4x^2

$$( 2 x - 3 ) ^ { 2 } = 5 x + 4 x ^ { 2 }$$

Solve for x

$$x=\frac{9}{17}\approx 0.529411765$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$4x^{2}-12x+9=5x+4x^{2}$$

Subtract 5x from both sides.

$$4x^{2}-12x+9-5x=4x^{2}$$

Combine -12x and -5x to get -17x.

$$4x^{2}-17x+9=4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}-17x+9-4x^{2}=0$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-17x+9=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-17x=-9$$

Divide both sides by -17.

$$x=\frac{-9}{-17}$$

Fraction \frac{-9}{-17} can be simplified to \frac{9}{17} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{17}$$