6x+x2=119

Solution for 6x+x2=119 equation:

6x+x2=119

We move all terms to the left:

6x+x2-(119)=0

We add all the numbers together, and all the variables

x^2+6x-119=0

a = 1; b = 6; c = -119;
Δ = b2-4ac
Δ = 62-4·1·(-119)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-16\sqrt{2}}{2*1}=\frac{-6-16\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+16\sqrt{2}}{2*1}=\frac{-6+16\sqrt{2}}{2}
$