(x^2+10x-78)=x+7

Solution for (x^2+10x-78)=x+7 equation:

(x^2+10x-78)=x+7

We move all terms to the left:

(x^2+10x-78)-(x+7)=0

We get rid of parentheses

x^2+10x-x-78-7=0

We add all the numbers together, and all the variables

x^2+9x-85=0

a = 1; b = 9; c = -85;
Δ = b2-4ac
Δ = 92-4·1·(-85)
Δ = 421
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{-(9)-\sqrt{421}}{2*1}=\frac{-9-\sqrt{421}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{421}}{2*1}=\frac{-9+\sqrt{421}}{2}
$