9x-3/4x=15

Solution for 9x-3/4x=15 equation:

9x-3/4x=15

We move all terms to the left:

9x-3/4x-(15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


9x*4x-15*4x-3=0

Wy multiply elements

36x^2-60x-3=0

a = 36; b = -60; c = -3;
Δ = b2-4ac
Δ = -602-4·36·(-3)
Δ = 4032
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-24\sqrt{7}}{2*36}=\frac{60-24\sqrt{7}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+24\sqrt{7}}{2*36}=\frac{60+24\sqrt{7}}{72}
$