8(1/3m+5)=1/2m-4

Solution for 8(1/3m+5)=1/2m-4 equation:

8(1/3m+5)=1/2m-4

We move all terms to the left:

8(1/3m+5)-(1/2m-4)=0


Domain of the equation: 3m+5)!=0

m∈R



Domain of the equation: 2m-4)!=0

m∈R


We multiply parentheses

8m-(1/2m-4)+40=0

We get rid of parentheses

8m-1/2m+4+40=0

We multiply all the terms by the denominator


8m*2m+4*2m+40*2m-1=0

Wy multiply elements

16m^2+8m+80m-1=0

We add all the numbers together, and all the variables

16m^2+88m-1=0

a = 16; b = 88; c = -1;
Δ = b2-4ac
Δ = 882-4·16·(-1)
Δ = 7808
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:

$\sqrt{\Delta}=\sqrt{7808}=\sqrt{64*122}=\sqrt{64}*\sqrt{122}=8\sqrt{122}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-8\sqrt{122}}{2*16}=\frac{-88-8\sqrt{122}}{32}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+8\sqrt{122}}{2*16}=\frac{-88+8\sqrt{122}}{32}
$