4x-5=4x^2-20x+25

Solution for 4x-5=4x^2-20x+25 equation:

4x-5=4x^2-20x+25

We move all terms to the left:

4x-5-(4x^2-20x+25)=0

We get rid of parentheses

-4x^2+4x+20x-25-5=0

We add all the numbers together, and all the variables

-4x^2+24x-30=0

a = -4; b = 24; c = -30;
Δ = b2-4ac
Δ = 242-4·(-4)·(-30)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{6}}{2*-4}=\frac{-24-4\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{6}}{2*-4}=\frac{-24+4\sqrt{6}}{-8}
$