-5x^2=-43x-18

Solution for -5x^2=-43x-18 equation:

-5x^2=-43x-18

We move all terms to the left:

-5x^2-(-43x-18)=0

We get rid of parentheses

-5x^2+43x+18=0

a = -5; b = 43; c = +18;
Δ = b2-4ac
Δ = 432-4·(-5)·18
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-47}{2*-5}=\frac{-90}{-10}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+47}{2*-5}=\frac{4}{-10}
=-2/5
$