5m^2=3+11m

Solution for 5m^2=3+11m equation:

5m^2=3+11m

We move all terms to the left:

5m^2-(3+11m)=0

We add all the numbers together, and all the variables

5m^2-(11m+3)=0

We get rid of parentheses

5m^2-11m-3=0

a = 5; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·5·(-3)
Δ = 181
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{-(-11)-\sqrt{181}}{2*5}=\frac{11-\sqrt{181}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{181}}{2*5}=\frac{11+\sqrt{181}}{10}
$