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(2x+3)-(5x-7)/6x+11=8/3
We move all terms to the left:
(2x+3)-(5x-7)/6x+11-(8/3)=0
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
(2x+3)-(5x-7)/6x+11-(+8/3)=0
We get rid of parentheses
2x-(5x-7)/6x+3+11-8/3=0
We calculate fractions
2x+(-15x+21)/18x+(-48x)/18x+3+11=0
We add all the numbers together, and all the variables
2x+(-15x+21)/18x+(-48x)/18x+14=0
We multiply all the terms by the denominator
2x*18x+(-15x+21)+(-48x)+14*18x=0
Wy multiply elements
36x^2+(-15x+21)+(-48x)+252x=0
We get rid of parentheses
36x^2-15x-48x+252x+21=0
We add all the numbers together, and all the variables
36x^2+189x+21=0
a = 36; b = 189; c = +21;
Δ = b2-4ac
Δ = 1892-4·36·21
Δ = 32697
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32697}=\sqrt{9*3633}=\sqrt{9}*\sqrt{3633}=3\sqrt{3633}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(189)-3\sqrt{3633}}{2*36}=\frac{-189-3\sqrt{3633}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(189)+3\sqrt{3633}}{2*36}=\frac{-189+3\sqrt{3633}}{72} $
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