7=3m^2+5m-2

Solution for 7=3m^2+5m-2 equation:

7=3m^2+5m-2

We move all terms to the left:

7-(3m^2+5m-2)=0

We get rid of parentheses

-3m^2-5m+2+7=0

We add all the numbers together, and all the variables

-3m^2-5m+9=0

a = -3; b = -5; c = +9;
Δ = b2-4ac
Δ = -52-4·(-3)·9
Δ = 133
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{-(-5)-\sqrt{133}}{2*-3}=\frac{5-\sqrt{133}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{133}}{2*-3}=\frac{5+\sqrt{133}}{-6}
$