7=3m^2+5m+5

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

7=3m^2+5m+5

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-3)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-3}=\frac{-2}{-6}
=1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-3}=\frac{12}{-6}
=-2
$