4m=3/4m-6

Solution for 4m=3/4m-6 equation:

4m=3/4m-6

We move all terms to the left:

4m-(3/4m-6)=0


Domain of the equation: 4m-6)!=0

m∈R


We get rid of parentheses

4m-3/4m+6=0

We multiply all the terms by the denominator


4m*4m+6*4m-3=0

Wy multiply elements

16m^2+24m-3=0

a = 16; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·16·(-3)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{3}}{2*16}=\frac{-24-16\sqrt{3}}{32}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{3}}{2*16}=\frac{-24+16\sqrt{3}}{32}
$