X^2-3x=15x+239

Solution for X^2-3x=15x+239 equation:

X^2-3X=15X+239

We move all terms to the left:

X^2-3X-(15X+239)=0

We get rid of parentheses

X^2-3X-15X-239=0

We add all the numbers together, and all the variables

X^2-18X-239=0

a = 1; b = -18; c = -239;
Δ = b2-4ac
Δ = -182-4·1·(-239)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-16\sqrt{5}}{2*1}=\frac{18-16\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+16\sqrt{5}}{2*1}=\frac{18+16\sqrt{5}}{2}
$