5m^2=8m+13

Solution for 5m^2=8m+13 equation:

5m^2=8m+13

We move all terms to the left:

5m^2-(8m+13)=0

We get rid of parentheses

5m^2-8m-13=0

a = 5; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·5·(-13)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-18}{2*5}=\frac{-10}{10}
=-1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+18}{2*5}=\frac{26}{10}
=2+3/5
$