18/56m-12=4m-6

Solution for 18/56m-12=4m-6 equation:

18/56m-12=4m-6

We move all terms to the left:

18/56m-12-(4m-6)=0


Domain of the equation: 56m!=0

m!=0/56

m!=0

m∈R


We get rid of parentheses

18/56m-4m+6-12=0

We multiply all the terms by the denominator


-4m*56m+6*56m-12*56m+18=0

Wy multiply elements

-224m^2+336m-672m+18=0

We add all the numbers together, and all the variables

-224m^2-336m+18=0

a = -224; b = -336; c = +18;
Δ = b2-4ac
Δ = -3362-4·(-224)·18
Δ = 129024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{129024}=\sqrt{9216*14}=\sqrt{9216}*\sqrt{14}=96\sqrt{14}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-96\sqrt{14}}{2*-224}=\frac{336-96\sqrt{14}}{-448}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+96\sqrt{14}}{2*-224}=\frac{336+96\sqrt{14}}{-448}
$