X2=6x+91

Solution for X2=6x+91 equation:

X2=6X+91

We move all terms to the left:

X2-(6X+91)=0

We add all the numbers together, and all the variables

X^2-(6X+91)=0

We get rid of parentheses

X^2-6X-91=0

a = 1; b = -6; c = -91;
Δ = b2-4ac
Δ = -62-4·1·(-91)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-20}{2*1}=\frac{-14}{2}
=-7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+20}{2*1}=\frac{26}{2}
=13
$