5x2-8x-5=15

Solution for 5x2-8x-5=15 equation:

5x^2-8x-5=15

We move all terms to the left:

5x^2-8x-5-(15)=0

We add all the numbers together, and all the variables

5x^2-8x-20=0

a = 5; b = -8; c = -20;
Δ = b2-4ac
Δ = -82-4·5·(-20)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{29}}{2*5}=\frac{8-4\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{29}}{2*5}=\frac{8+4\sqrt{29}}{10}
$