x^2-15x-78=34

Solution for x^2-15x-78=34 equation:

x^2-15x-78=34

We move all terms to the left:

x^2-15x-78-(34)=0

We add all the numbers together, and all the variables

x^2-15x-112=0

a = 1; b = -15; c = -112;
Δ = b2-4ac
Δ = -152-4·1·(-112)
Δ = 673
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{673}}{2*1}=\frac{15-\sqrt{673}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{673}}{2*1}=\frac{15+\sqrt{673}}{2}
$