1/5m+8=3m-20

Solution for 1/5m+8=3m-20 equation:

1/5m+8=3m-20

We move all terms to the left:

1/5m+8-(3m-20)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We get rid of parentheses

1/5m-3m+20+8=0

We multiply all the terms by the denominator


-3m*5m+20*5m+8*5m+1=0

Wy multiply elements

-15m^2+100m+40m+1=0

We add all the numbers together, and all the variables

-15m^2+140m+1=0

a = -15; b = 140; c = +1;
Δ = b2-4ac
Δ = 1402-4·(-15)·1
Δ = 19660
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:

$\sqrt{\Delta}=\sqrt{19660}=\sqrt{4*4915}=\sqrt{4}*\sqrt{4915}=2\sqrt{4915}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-2\sqrt{4915}}{2*-15}=\frac{-140-2\sqrt{4915}}{-30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+2\sqrt{4915}}{2*-15}=\frac{-140+2\sqrt{4915}}{-30}
$