2(x-2)(x+2)^2=5x-7

Solution for 2(x-2)(x+2)^2=5x-7 equation:

2(x-2)(x+2)^2=5x-7

We move all terms to the left:

2(x-2)(x+2)^2-(5x-7)=0

We use the square of the difference formula

x^2-(5x-7)-4=0

We get rid of parentheses

x^2-5x+7-4=0

We add all the numbers together, and all the variables

x^2-5x+3=0

a = 1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·1·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{13}}{2*1}=\frac{5-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*1}=\frac{5+\sqrt{13}}{2}
$