0=5x^2+75x-130

Solution for 0=5x^2+75x-130 equation:

0=5x^2+75x-130

We move all terms to the left:

0-(5x^2+75x-130)=0

We add all the numbers together, and all the variables

-(5x^2+75x-130)=0

We get rid of parentheses

-5x^2-75x+130=0

a = -5; b = -75; c = +130;
Δ = b2-4ac
Δ = -752-4·(-5)·130
Δ = 8225
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:

$\sqrt{\Delta}=\sqrt{8225}=\sqrt{25*329}=\sqrt{25}*\sqrt{329}=5\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{329}}{2*-5}=\frac{75-5\sqrt{329}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{329}}{2*-5}=\frac{75+5\sqrt{329}}{-10}
$