x^2+30x-400=x+10

Solution for x^2+30x-400=x+10 equation:

x^2+30x-400=x+10

We move all terms to the left:

x^2+30x-400-(x+10)=0

We get rid of parentheses

x^2+30x-x-10-400=0

We add all the numbers together, and all the variables

x^2+29x-410=0

a = 1; b = 29; c = -410;
Δ = b2-4ac
Δ = 292-4·1·(-410)
Δ = 2481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{2481}}{2*1}=\frac{-29-\sqrt{2481}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{2481}}{2*1}=\frac{-29+\sqrt{2481}}{2}
$