X^2+11x=8

Solution for X^2+11x=8 equation:

X^2+11X=8

We move all terms to the left:

X^2+11X-(8)=0

a = 1; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·1·(-8)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{17}}{2*1}=\frac{-11-3\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{17}}{2*1}=\frac{-11+3\sqrt{17}}{2}
$