14+7/2m=10+4m

Solution for 14+7/2m=10+4m equation:

14+7/2m=10+4m

We move all terms to the left:

14+7/2m-(10+4m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

7/2m-(4m+10)+14=0

We get rid of parentheses

7/2m-4m-10+14=0

We multiply all the terms by the denominator


-4m*2m-10*2m+14*2m+7=0

Wy multiply elements

-8m^2-20m+28m+7=0

We add all the numbers together, and all the variables

-8m^2+8m+7=0

a = -8; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·(-8)·7
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{2}}{2*-8}=\frac{-8-12\sqrt{2}}{-16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{2}}{2*-8}=\frac{-8+12\sqrt{2}}{-16}
$