m=4.75/4m-7

Solution for m=4.75/4m-7 equation:

m=4.75/4m-7

We move all terms to the left:

m-(4.75/4m-7)=0


Domain of the equation: 4m-7)!=0

m∈R


We get rid of parentheses

m-4.75/4m+7=0

We multiply all the terms by the denominator


m*4m+7*4m-4.75=0

Wy multiply elements

4m^2+28m-4.75=0

a = 4; b = 28; c = -4.75;
Δ = b2-4ac
Δ = 282-4·4·(-4.75)
Δ = 860
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:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{215}}{2*4}=\frac{-28-2\sqrt{215}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{215}}{2*4}=\frac{-28+2\sqrt{215}}{8}
$