-78g^2=-32g+2

Solution for -78g^2=-32g+2 equation:

-78g^2=-32g+2

We move all terms to the left:

-78g^2-(-32g+2)=0

We get rid of parentheses

-78g^2+32g-2=0

a = -78; b = 32; c = -2;
Δ = b2-4ac
Δ = 322-4·(-78)·(-2)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-20}{2*-78}=\frac{-52}{-156}
=1/3
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+20}{2*-78}=\frac{-12}{-156}
=1/13
$