-4x+52-26x-13=-8x^2+104x

Solution for -4x+52-26x-13=-8x^2+104x equation:

-4x+52-26x-13=-8x^2+104x

We move all terms to the left:

-4x+52-26x-13-(-8x^2+104x)=0

We add all the numbers together, and all the variables

-(-8x^2+104x)-30x+39=0

We get rid of parentheses

8x^2-104x-30x+39=0

We add all the numbers together, and all the variables

8x^2-134x+39=0

a = 8; b = -134; c = +39;
Δ = b2-4ac
Δ = -1342-4·8·39
Δ = 16708
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:

$\sqrt{\Delta}=\sqrt{16708}=\sqrt{4*4177}=\sqrt{4}*\sqrt{4177}=2\sqrt{4177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134)-2\sqrt{4177}}{2*8}=\frac{134-2\sqrt{4177}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134)+2\sqrt{4177}}{2*8}=\frac{134+2\sqrt{4177}}{16}
$