3m^2-8=-5m

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

3m^2-8=-5m

We move all terms to the left:

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

We get rid of parentheses

3m^2+5m-8=0

a = 3; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*3}=\frac{-16}{6}
=-2+2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*3}=\frac{6}{6}
=1
$