15x^2+104x-83=5

Solution for 15x^2+104x-83=5 equation:

15x^2+104x-83=5

We move all terms to the left:

15x^2+104x-83-(5)=0

We add all the numbers together, and all the variables

15x^2+104x-88=0

a = 15; b = 104; c = -88;
Δ = b2-4ac
Δ = 1042-4·15·(-88)
Δ = 16096
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:

$\sqrt{\Delta}=\sqrt{16096}=\sqrt{16*1006}=\sqrt{16}*\sqrt{1006}=4\sqrt{1006}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-4\sqrt{1006}}{2*15}=\frac{-104-4\sqrt{1006}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+4\sqrt{1006}}{2*15}=\frac{-104+4\sqrt{1006}}{30}
$