-5x^2=2x-39

Solution for -5x^2=2x-39 equation:

-5x^2=2x-39

We move all terms to the left:

-5x^2-(2x-39)=0

We get rid of parentheses

-5x^2-2x+39=0

a = -5; b = -2; c = +39;
Δ = b2-4ac
Δ = -22-4·(-5)·39
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-28}{2*-5}=\frac{-26}{-10}
=2+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+28}{2*-5}=\frac{30}{-10}
=-3
$