x2+30x+150=250

Solution for x2+30x+150=250 equation:

x2+30x+150=250

We move all terms to the left:

x2+30x+150-(250)=0

We add all the numbers together, and all the variables

x^2+30x-100=0

a = 1; b = 30; c = -100;
Δ = b2-4ac
Δ = 302-4·1·(-100)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{13}}{2*1}=\frac{-30-10\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{13}}{2*1}=\frac{-30+10\sqrt{13}}{2}
$