-5x^2-114=50x-9

Solution for -5x^2-114=50x-9 equation:

-5x^2-114=50x-9

We move all terms to the left:

-5x^2-114-(50x-9)=0

We get rid of parentheses

-5x^2-50x+9-114=0

We add all the numbers together, and all the variables

-5x^2-50x-105=0

a = -5; b = -50; c = -105;
Δ = b2-4ac
Δ = -502-4·(-5)·(-105)
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{-(-50)-20}{2*-5}=\frac{30}{-10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20}{2*-5}=\frac{70}{-10}
=-7
$