3/2m-10=8-m

Solution for 3/2m-10=8-m equation:

3/2m-10=8-m

We move all terms to the left:

3/2m-10-(8-m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

3/2m-(-1m+8)-10=0

We get rid of parentheses

3/2m+1m-8-10=0

We multiply all the terms by the denominator


1m*2m-8*2m-10*2m+3=0

Wy multiply elements

2m^2-16m-20m+3=0

We add all the numbers together, and all the variables

2m^2-36m+3=0

a = 2; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·2·3
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{318}}{2*2}=\frac{36-2\sqrt{318}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{318}}{2*2}=\frac{36+2\sqrt{318}}{4}
$