21m^2-140m=-84

Solution for 21m^2-140m=-84 equation:

21m^2-140m=-84

We move all terms to the left:

21m^2-140m-(-84)=0

We add all the numbers together, and all the variables

21m^2-140m+84=0

a = 21; b = -140; c = +84;
Δ = b2-4ac
Δ = -1402-4·21·84
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-112}{2*21}=\frac{28}{42}
=2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+112}{2*21}=\frac{252}{42}
=6
$