X=9x-9/2x+7

Solution for X=9x-9/2x+7 equation:

X=9X-9/2X+7

We move all terms to the left:

X-(9X-9/2X+7)=0


Domain of the equation: 2X+7)!=0

X∈R


We get rid of parentheses

X-9X+9/2X-7=0

We multiply all the terms by the denominator


X*2X-9X*2X-7*2X+9=0

Wy multiply elements

2X^2-18X^2-14X+9=0

We add all the numbers together, and all the variables

-16X^2-14X+9=0

a = -16; b = -14; c = +9;
Δ = b2-4ac
Δ = -142-4·(-16)·9
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{193}}{2*-16}=\frac{14-2\sqrt{193}}{-32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{193}}{2*-16}=\frac{14+2\sqrt{193}}{-32}
$