4m^2-3m=2

Solution for 4m^2-3m=2 equation:

4m^2-3m=2

We move all terms to the left:

4m^2-3m-(2)=0

a = 4; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·4·(-2)
Δ = 41
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{-(-3)-\sqrt{41}}{2*4}=\frac{3-\sqrt{41}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*4}=\frac{3+\sqrt{41}}{8}
$