X^2+8x=9(9+11)

Solution for X^2+8x=9(9+11) equation:

X^2+8X=9(9+11)

We move all terms to the left:

X^2+8X-(9(9+11))=0

We add all the numbers together, and all the variables

X^2+8X-(920)=0

We add all the numbers together, and all the variables

X^2+8X-920=0

a = 1; b = 8; c = -920;
Δ = b2-4ac
Δ = 82-4·1·(-920)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{26}}{2*1}=\frac{-8-12\sqrt{26}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{26}}{2*1}=\frac{-8+12\sqrt{26}}{2}
$