-40x^2-2x=-38

Solution for -40x^2-2x=-38 equation:

-40x^2-2x=-38

We move all terms to the left:

-40x^2-2x-(-38)=0

We add all the numbers together, and all the variables

-40x^2-2x+38=0

a = -40; b = -2; c = +38;
Δ = b2-4ac
Δ = -22-4·(-40)·38
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-78}{2*-40}=\frac{-76}{-80}
=19/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+78}{2*-40}=\frac{80}{-80}
=-1
$