-2m^2=-102-5m

Solution for -2m^2=-102-5m equation:

-2m^2=-102-5m

We move all terms to the left:

-2m^2-(-102-5m)=0

We add all the numbers together, and all the variables

-2m^2-(-5m-102)=0

We get rid of parentheses

-2m^2+5m+102=0

a = -2; b = 5; c = +102;
Δ = b2-4ac
Δ = 52-4·(-2)·102
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*-2}=\frac{-34}{-4}
=8+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*-2}=\frac{24}{-4}
=-6
$