15x^2-2x-8=300

Solution for 15x^2-2x-8=300 equation:

15x^2-2x-8=300

We move all terms to the left:

15x^2-2x-8-(300)=0

We add all the numbers together, and all the variables

15x^2-2x-308=0

a = 15; b = -2; c = -308;
Δ = b2-4ac
Δ = -22-4·15·(-308)
Δ = 18484
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:

$\sqrt{\Delta}=\sqrt{18484}=\sqrt{4*4621}=\sqrt{4}*\sqrt{4621}=2\sqrt{4621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{4621}}{2*15}=\frac{2-2\sqrt{4621}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{4621}}{2*15}=\frac{2+2\sqrt{4621}}{30}
$