5x^2-58x-80=0

Solution for 5x^2-58x-80=0 equation:

5x^2-58x-80=0

a = 5; b = -58; c = -80;
Δ = b2-4ac
Δ = -582-4·5·(-80)
Δ = 4964
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:

$\sqrt{\Delta}=\sqrt{4964}=\sqrt{4*1241}=\sqrt{4}*\sqrt{1241}=2\sqrt{1241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{1241}}{2*5}=\frac{58-2\sqrt{1241}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{1241}}{2*5}=\frac{58+2\sqrt{1241}}{10}
$