9m-4/2m-3=7

Solution for 9m-4/2m-3=7 equation:

9m-4/2m-3=7

We move all terms to the left:

9m-4/2m-3-(7)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

9m-4/2m-10=0

We multiply all the terms by the denominator


9m*2m-10*2m-4=0

Wy multiply elements

18m^2-20m-4=0

a = 18; b = -20; c = -4;
Δ = b2-4ac
Δ = -202-4·18·(-4)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{43}}{2*18}=\frac{20-4\sqrt{43}}{36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{43}}{2*18}=\frac{20+4\sqrt{43}}{36}
$