5m^2-3m=13

Solution for 5m^2-3m=13 equation:

5m^2-3m=13

We move all terms to the left:

5m^2-3m-(13)=0

a = 5; b = -3; c = -13;
Δ = b2-4ac
Δ = -32-4·5·(-13)
Δ = 269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{269}}{2*5}=\frac{3-\sqrt{269}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{269}}{2*5}=\frac{3+\sqrt{269}}{10}
$