10x+150+10x=x^2+15

Solution for 10x+150+10x=x^2+15 equation:

10x+150+10x=x^2+15

We move all terms to the left:

10x+150+10x-(x^2+15)=0

We add all the numbers together, and all the variables

20x-(x^2+15)+150=0

We get rid of parentheses

-x^2+20x-15+150=0

We add all the numbers together, and all the variables

-1x^2+20x+135=0

a = -1; b = 20; c = +135;
Δ = b2-4ac
Δ = 202-4·(-1)·135
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{235}}{2*-1}=\frac{-20-2\sqrt{235}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{235}}{2*-1}=\frac{-20+2\sqrt{235}}{-2}
$