20/(m+5)+35=7m

Solution for 20/(m+5)+35=7m equation:

20/(m+5)+35=7m

We move all terms to the left:

20/(m+5)+35-(7m)=0


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

We move all terms containing m to the left, all other terms to the right

m!=-5

m∈R


We add all the numbers together, and all the variables

-7m+20/(m+5)+35=0

We multiply all the terms by the denominator


-7m*(m+5)+35*(m+5)+20=0

We multiply parentheses

-7m^2-35m+35m+175+20=0

We add all the numbers together, and all the variables

-7m^2+195=0

a = -7; b = 0; c = +195;
Δ = b2-4ac
Δ = 02-4·(-7)·195
Δ = 5460
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:

$\sqrt{\Delta}=\sqrt{5460}=\sqrt{4*1365}=\sqrt{4}*\sqrt{1365}=2\sqrt{1365}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1365}}{2*-7}=\frac{0-2\sqrt{1365}}{-14}
=-\frac{2\sqrt{1365}}{-14}
=-\frac{\sqrt{1365}}{-7}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1365}}{2*-7}=\frac{0+2\sqrt{1365}}{-14}
=\frac{2\sqrt{1365}}{-14}
=\frac{\sqrt{1365}}{-7}
$