5x2+60x-415=0

Solution for 5x2+60x-415=0 equation:

5x^2+60x-415=0

a = 5; b = 60; c = -415;
Δ = b2-4ac
Δ = 602-4·5·(-415)
Δ = 11900
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:

$\sqrt{\Delta}=\sqrt{11900}=\sqrt{100*119}=\sqrt{100}*\sqrt{119}=10\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-10\sqrt{119}}{2*5}=\frac{-60-10\sqrt{119}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+10\sqrt{119}}{2*5}=\frac{-60+10\sqrt{119}}{10}
$