3m^2=8m-5

Solution for 3m^2=8m-5 equation:

3m^2=8m-5

We move all terms to the left:

3m^2-(8m-5)=0

We get rid of parentheses

3m^2-8m+5=0

a = 3; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·3·5
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*3}=\frac{6}{6}
=1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*3}=\frac{10}{6}
=1+2/3
$