x^2-34=-15x

Solution for x^2-34=-15x equation:

x^2-34=-15x

We move all terms to the left:

x^2-34-(-15x)=0

We get rid of parentheses

x^2+15x-34=0

a = 1; b = 15; c = -34;
Δ = b2-4ac
Δ = 152-4·1·(-34)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-19}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+19}{2*1}=\frac{4}{2}
=2
$