-4(5x2+3)=-52

Solution for -4(5x2+3)=-52 equation:

-4(5x^2+3)=-52

We move all terms to the left:

-4(5x^2+3)-(-52)=0

We add all the numbers together, and all the variables

-4(5x^2+3)+52=0

We multiply parentheses

-20x^2-12+52=0

We add all the numbers together, and all the variables

-20x^2+40=0

a = -20; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-20)·40
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*-20}=\frac{0-40\sqrt{2}}{-40}
=-\frac{40\sqrt{2}}{-40}
=-\frac{\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*-20}=\frac{0+40\sqrt{2}}{-40}
=\frac{40\sqrt{2}}{-40}
=\frac{\sqrt{2}}{-1}
$