(g-2)(g+5)=-7

Solution for (g-2)(g+5)=-7 equation:

(g-2)(g+5)=-7

We move all terms to the left:

(g-2)(g+5)-(-7)=0

We add all the numbers together, and all the variables

(g-2)(g+5)+7=0

We multiply parentheses ..

(+g^2+5g-2g-10)+7=0

We get rid of parentheses

g^2+5g-2g-10+7=0

We add all the numbers together, and all the variables

g^2+3g-3=0

a = 1; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·1·(-3)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{21}}{2*1}=\frac{-3-\sqrt{21}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*1}=\frac{-3+\sqrt{21}}{2}
$