5x^2-4(x^2-2x+1)-5=0

Solution for 5x^2-4(x^2-2x+1)-5=0 equation:

5x^2-4(x^2-2x+1)-5=0

We multiply parentheses

5x^2-4x^2+8x-4-5=0

We add all the numbers together, and all the variables

x^2+8x-9=0

a = 1; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·1·(-9)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*1}=\frac{2}{2}
=1
$