4m^2+10m=6

Solution for 4m^2+10m=6 equation:

4m^2+10m=6

We move all terms to the left:

4m^2+10m-(6)=0

a = 4; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·4·(-6)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*4}=\frac{-24}{8}
=-3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*4}=\frac{4}{8}
=1/2
$