9x-3/2x=4

Solution for 9x-3/2x=4 equation:

9x-3/2x=4

We move all terms to the left:

9x-3/2x-(4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


9x*2x-4*2x-3=0

Wy multiply elements

18x^2-8x-3=0

a = 18; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·18·(-3)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{70}}{2*18}=\frac{8-2\sqrt{70}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{70}}{2*18}=\frac{8+2\sqrt{70}}{36}
$