X^2=15x+2

Solution for X^2=15x+2 equation:

X^2=15X+2

We move all terms to the left:

X^2-(15X+2)=0

We get rid of parentheses

X^2-15X-2=0

a = 1; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·1·(-2)
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{233}}{2*1}=\frac{15-\sqrt{233}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{233}}{2*1}=\frac{15+\sqrt{233}}{2}
$