7m^2-2m=5

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

7m^2-2m=5

We move all terms to the left:

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

a = 7; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·7·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*7}=\frac{-10}{14}
=-5/7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*7}=\frac{14}{14}
=1
$