15x2+15x-78=0

Solution for 15x2+15x-78=0 equation:

15x^2+15x-78=0

a = 15; b = 15; c = -78;
Δ = b2-4ac
Δ = 152-4·15·(-78)
Δ = 4905
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:

$\sqrt{\Delta}=\sqrt{4905}=\sqrt{9*545}=\sqrt{9}*\sqrt{545}=3\sqrt{545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{545}}{2*15}=\frac{-15-3\sqrt{545}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{545}}{2*15}=\frac{-15+3\sqrt{545}}{30}
$