g^2+7g+12.25=144

Solution for g^2+7g+12.25=144 equation:

g^2+7g+12.25=144

We move all terms to the left:

g^2+7g+12.25-(144)=0

We add all the numbers together, and all the variables

g^2+7g-131.75=0

a = 1; b = 7; c = -131.75;
Δ = b2-4ac
Δ = 72-4·1·(-131.75)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-24}{2*1}=\frac{-31}{2}
=-15+1/2
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+24}{2*1}=\frac{17}{2}
=8+1/2
$