116+10x=x^2

Solution for 116+10x=x^2 equation:

116+10x=x^2

We move all terms to the left:

116+10x-(x^2)=0

determiningTheFunctionDomain
-x^2+10x+116=0

We add all the numbers together, and all the variables

-1x^2+10x+116=0

a = -1; b = 10; c = +116;
Δ = b2-4ac
Δ = 102-4·(-1)·116
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{141}}{2*-1}=\frac{-10-2\sqrt{141}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{141}}{2*-1}=\frac{-10+2\sqrt{141}}{-2}
$