x^2-5x-78=-15

Solution for x^2-5x-78=-15 equation:

x^2-5x-78=-15

We move all terms to the left:

x^2-5x-78-(-15)=0

We add all the numbers together, and all the variables

x^2-5x-63=0

a = 1; b = -5; c = -63;
Δ = b2-4ac
Δ = -52-4·1·(-63)
Δ = 277
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{-(-5)-\sqrt{277}}{2*1}=\frac{5-\sqrt{277}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{277}}{2*1}=\frac{5+\sqrt{277}}{2}
$