(2x+13)-15=(3x)^2-217

Solution for (2x+13)-15=(3x)^2-217 equation:

(2x+13)-15=(3x)^2-217

We move all terms to the left:

(2x+13)-15-((3x)^2-217)=0

We get rid of parentheses

-3x^2+2x+13+217-15=0

We add all the numbers together, and all the variables

-3x^2+2x+215=0

a = -3; b = 2; c = +215;
Δ = b2-4ac
Δ = 22-4·(-3)·215
Δ = 2584
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:

$\sqrt{\Delta}=\sqrt{2584}=\sqrt{4*646}=\sqrt{4}*\sqrt{646}=2\sqrt{646}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{646}}{2*-3}=\frac{-2-2\sqrt{646}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{646}}{2*-3}=\frac{-2+2\sqrt{646}}{-6}
$