3x-3=11/2x+9

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



3x-3=11/2x+9
We move all terms to the left:
3x-3-(11/2x+9)=0
Domain of the equation: 2x+9)!=0
x∈R
We get rid of parentheses
3x-11/2x-9-3=0
We multiply all the terms by the denominator
3x*2x-9*2x-3*2x-11=0
Wy multiply elements
6x^2-18x-6x-11=0
We add all the numbers together, and all the variables
6x^2-24x-11=0
a = 6; b = -24; c = -11;
Δ = b2-4ac
Δ = -242-4·6·(-11)
Δ = 840
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:
$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{210}}{2*6}=\frac{24-2\sqrt{210}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{210}}{2*6}=\frac{24+2\sqrt{210}}{12} $

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