P=5m^2+12m+2

Solution for P=5m^2+12m+2 equation:

=5P^2+12P+2

We move all terms to the left:

-(5P^2+12P+2)=0

We get rid of parentheses

-5P^2-12P-2=0

a = -5; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·(-5)·(-2)
Δ = 104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{26}}{2*-5}=\frac{12-2\sqrt{26}}{-10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{26}}{2*-5}=\frac{12+2\sqrt{26}}{-10}
$