m=1/4m+5=3/8m+4

Solution for m=1/4m+5=3/8m+4 equation:

m=1/4m+5=3/8m+4

We move all terms to the left:

m-(1/4m+5)=0


Domain of the equation: 4m+5)!=0

m∈R


We get rid of parentheses

m-1/4m-5=0

We multiply all the terms by the denominator


m*4m-5*4m-1=0

Wy multiply elements

4m^2-20m-1=0

a = 4; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·4·(-1)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*4}=\frac{20-4\sqrt{26}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*4}=\frac{20+4\sqrt{26}}{8}
$