15x-5x^2+130=0

Solution for 15x-5x^2+130=0 equation:

15x-5x^2+130=0

a = -5; b = 15; c = +130;
Δ = b2-4ac
Δ = 152-4·(-5)·130
Δ = 2825
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:

$\sqrt{\Delta}=\sqrt{2825}=\sqrt{25*113}=\sqrt{25}*\sqrt{113}=5\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{113}}{2*-5}=\frac{-15-5\sqrt{113}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{113}}{2*-5}=\frac{-15+5\sqrt{113}}{-10}
$