X=10/2x-9

Solution for X=10/2x-9 equation:

X=10/2X-9

We move all terms to the left:

X-(10/2X-9)=0


Domain of the equation: 2X-9)!=0

X∈R


We get rid of parentheses

X-10/2X+9=0

We multiply all the terms by the denominator


X*2X+9*2X-10=0

Wy multiply elements

2X^2+18X-10=0

a = 2; b = 18; c = -10;
Δ = b2-4ac
Δ = 182-4·2·(-10)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{101}}{2*2}=\frac{-18-2\sqrt{101}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{101}}{2*2}=\frac{-18+2\sqrt{101}}{4}
$