x2+17x+72=12

Solution for x2+17x+72=12 equation:

x2+17x+72=12

We move all terms to the left:

x2+17x+72-(12)=0

We add all the numbers together, and all the variables

x^2+17x+60=0

a = 1; b = 17; c = +60;
Δ = b2-4ac
Δ = 172-4·1·60
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*1}=\frac{-10}{2}
=-5
$