258-3/8m=5m

Solution for 258-3/8m=5m equation:

258-3/8m=5m

We move all terms to the left:

258-3/8m-(5m)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R


We add all the numbers together, and all the variables

-5m-3/8m+258=0

We multiply all the terms by the denominator


-5m*8m+258*8m-3=0

Wy multiply elements

-40m^2+2064m-3=0

a = -40; b = 2064; c = -3;
Δ = b2-4ac
Δ = 20642-4·(-40)·(-3)
Δ = 4259616
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:

$\sqrt{\Delta}=\sqrt{4259616}=\sqrt{16*266226}=\sqrt{16}*\sqrt{266226}=4\sqrt{266226}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2064)-4\sqrt{266226}}{2*-40}=\frac{-2064-4\sqrt{266226}}{-80}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2064)+4\sqrt{266226}}{2*-40}=\frac{-2064+4\sqrt{266226}}{-80}
$