5x^2-4(2x^2-13x)=0

Solution for 5x^2-4(2x^2-13x)=0 equation:

5x^2-4(2x^2-13x)=0

We multiply parentheses

5x^2-8x^2+52x=0

We add all the numbers together, and all the variables

-3x^2+52x=0

a = -3; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-3)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-3}=\frac{-104}{-6}
=17+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-3}=\frac{0}{-6}
=0
$