15x^2-7x-20=x

Solution for 15x^2-7x-20=x equation:

15x^2-7x-20=x

We move all terms to the left:

15x^2-7x-20-(x)=0

We add all the numbers together, and all the variables

15x^2-8x-20=0

a = 15; b = -8; c = -20;
Δ = b2-4ac
Δ = -82-4·15·(-20)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{79}}{2*15}=\frac{8-4\sqrt{79}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{79}}{2*15}=\frac{8+4\sqrt{79}}{30}
$