x-4/2x-9=0

Solution for x-4/2x-9=0 equation:

x-4/2x-9=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-18x-4=0

a = 2; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·2·(-4)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{89}}{2*2}=\frac{18-2\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{89}}{2*2}=\frac{18+2\sqrt{89}}{4}
$