6m^2-7m=10

Solution for 6m^2-7m=10 equation:

6m^2-7m=10

We move all terms to the left:

6m^2-7m-(10)=0

a = 6; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·6·(-10)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*6}=\frac{-10}{12}
=-5/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*6}=\frac{24}{12}
=2
$