5m^2-2m=7

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

5m^2-2m=7

We move all terms to the left:

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

a = 5; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·5·(-7)
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*5}=\frac{-10}{10}
=-1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*5}=\frac{14}{10}
=1+2/5
$