18g^2+24g=10

Solution for 18g^2+24g=10 equation:

18g^2+24g=10

We move all terms to the left:

18g^2+24g-(10)=0

a = 18; b = 24; c = -10;
Δ = b2-4ac
Δ = 242-4·18·(-10)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-36}{2*18}=\frac{-60}{36}
=-1+2/3
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+36}{2*18}=\frac{12}{36}
=1/3
$