13x^2-40x=80

Solution for 13x^2-40x=80 equation:

13x^2-40x=80

We move all terms to the left:

13x^2-40x-(80)=0

a = 13; b = -40; c = -80;
Δ = b2-4ac
Δ = -402-4·13·(-80)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-24\sqrt{10}}{2*13}=\frac{40-24\sqrt{10}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+24\sqrt{10}}{2*13}=\frac{40+24\sqrt{10}}{26}
$