4m-7/2m=18

Solution for 4m-7/2m=18 equation:

4m-7/2m=18

We move all terms to the left:

4m-7/2m-(18)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We multiply all the terms by the denominator


4m*2m-18*2m-7=0

Wy multiply elements

8m^2-36m-7=0

a = 8; b = -36; c = -7;
Δ = b2-4ac
Δ = -362-4·8·(-7)
Δ = 1520
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:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{95}}{2*8}=\frac{36-4\sqrt{95}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{95}}{2*8}=\frac{36+4\sqrt{95}}{16}
$