18g^2+5g-6=3g^2+27g-14

Solution for 18g^2+5g-6=3g^2+27g-14 equation:

18g^2+5g-6=3g^2+27g-14

We move all terms to the left:

18g^2+5g-6-(3g^2+27g-14)=0

We get rid of parentheses

18g^2-3g^2+5g-27g+14-6=0

We add all the numbers together, and all the variables

15g^2-22g+8=0

a = 15; b = -22; c = +8;
Δ = b2-4ac
Δ = -222-4·15·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2}{2*15}=\frac{20}{30}
=2/3
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2}{2*15}=\frac{24}{30}
=4/5
$