27x+50=x^2+27x-50

Solution for 27x+50=x^2+27x-50 equation:

27x+50=x^2+27x-50

We move all terms to the left:

27x+50-(x^2+27x-50)=0

We get rid of parentheses

-x^2+27x-27x+50+50=0

We add all the numbers together, and all the variables

-1x^2+100=0

a = -1; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-1)·100
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-1}=\frac{20}{-2}
=-10
$