-x^2+29x+30=10

Solution for -x^2+29x+30=10 equation:

-x^2+29x+30=10

We move all terms to the left:

-x^2+29x+30-(10)=0

We add all the numbers together, and all the variables

-1x^2+29x+20=0

a = -1; b = 29; c = +20;
Δ = b2-4ac
Δ = 292-4·(-1)·20
Δ = 921
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{921}}{2*-1}=\frac{-29-\sqrt{921}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{921}}{2*-1}=\frac{-29+\sqrt{921}}{-2}
$