5m2=-4m+13

Solution for 5m2=-4m+13 equation:

5m^2=-4m+13

We move all terms to the left:

5m^2-(-4m+13)=0

We get rid of parentheses

5m^2+4m-13=0

a = 5; b = 4; c = -13;
Δ = b2-4ac
Δ = 42-4·5·(-13)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{69}}{2*5}=\frac{-4-2\sqrt{69}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{69}}{2*5}=\frac{-4+2\sqrt{69}}{10}
$