5g+15=g2+21

Solution for 5g+15=g2+21 equation:

5g+15=g2+21

We move all terms to the left:

5g+15-(g2+21)=0

We add all the numbers together, and all the variables

-(+g^2+21)+5g+15=0

We get rid of parentheses

-g^2+5g-21+15=0

We add all the numbers together, and all the variables

-1g^2+5g-6=0

a = -1; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·(-1)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*-1}=\frac{-6}{-2}
=+3
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*-1}=\frac{-4}{-2}
=+2
$