2(2x-2)=1-5x2+5

Solution for 2(2x-2)=1-5x2+5 equation:

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2+4x-10=0

a = 5; b = 4; c = -10;
Δ = b2-4ac
Δ = 42-4·5·(-10)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{6}}{2*5}=\frac{-4-6\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{6}}{2*5}=\frac{-4+6\sqrt{6}}{10}
$