5x^2-8x=80

Solution for 5x^2-8x=80 equation:

5x^2-8x=80

We move all terms to the left:

5x^2-8x-(80)=0

a = 5; b = -8; c = -80;
Δ = b2-4ac
Δ = -82-4·5·(-80)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{26}}{2*5}=\frac{8-8\sqrt{26}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{26}}{2*5}=\frac{8+8\sqrt{26}}{10}
$