9/2x+12=3x+11-x

Solution for 9/2x+12=3x+11-x equation:

9/2x+12=3x+11-x

We move all terms to the left:

9/2x+12-(3x+11-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

9/2x-(2x+11)+12=0

We get rid of parentheses

9/2x-2x-11+12=0

We multiply all the terms by the denominator


-2x*2x-11*2x+12*2x+9=0

Wy multiply elements

-4x^2-22x+24x+9=0

We add all the numbers together, and all the variables

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

a = -4; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-4)·9
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*-4}=\frac{-2-2\sqrt{37}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*-4}=\frac{-2+2\sqrt{37}}{-8}
$