2x^2+30x+111=x^2

Solution for 2x^2+30x+111=x^2 equation:

2x^2+30x+111=x^2

We move all terms to the left:

2x^2+30x+111-(x^2)=0

determiningTheFunctionDomain
2x^2-x^2+30x+111=0

We add all the numbers together, and all the variables

x^2+30x+111=0

a = 1; b = 30; c = +111;
Δ = b2-4ac
Δ = 302-4·1·111
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{114}}{2*1}=\frac{-30-2\sqrt{114}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{114}}{2*1}=\frac{-30+2\sqrt{114}}{2}
$