-12m^2-372=-12+14m-17m^2

Solution for -12m^2-372=-12+14m-17m^2 equation:

-12m^2-372=-12+14m-17m^2

We move all terms to the left:

-12m^2-372-(-12+14m-17m^2)=0

We get rid of parentheses

-12m^2+17m^2-14m+12-372=0

We add all the numbers together, and all the variables

5m^2-14m-360=0

a = 5; b = -14; c = -360;
Δ = b2-4ac
Δ = -142-4·5·(-360)
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-86}{2*5}=\frac{-72}{10}
=-7+1/5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+86}{2*5}=\frac{100}{10}
=10
$