M4=13m2-36

Solution for M4=13m2-36 equation:

4=13M^2-36

We move all terms to the left:

4-(13M^2-36)=0

We get rid of parentheses

-13M^2+36+4=0

We add all the numbers together, and all the variables

-13M^2+40=0

a = -13; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-13)·40
Δ = 2080
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$M_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{130}}{2*-13}=\frac{0-4\sqrt{130}}{-26}
=-\frac{4\sqrt{130}}{-26}
=-\frac{2\sqrt{130}}{-13}
$
$M_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{130}}{2*-13}=\frac{0+4\sqrt{130}}{-26}
=\frac{4\sqrt{130}}{-26}
=\frac{2\sqrt{130}}{-13}
$