x=9/2x-4

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

x=9/2x-4

We move all terms to the left:

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


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

x-9/2x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+8x-9=0

a = 2; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·2·(-9)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*2}=\frac{-8-2\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*2}=\frac{-8+2\sqrt{34}}{4}
$