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(2x+3)-(5x+7)/6x+11=8/15
We move all terms to the left:
(2x+3)-(5x+7)/6x+11-(8/15)=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-(+8/15)=0
We get rid of parentheses
2x-(5x+7)/6x+3+11-8/15=0
We calculate fractions
2x+(-75x-105)/90x+(-48x)/90x+3+11=0
We add all the numbers together, and all the variables
2x+(-75x-105)/90x+(-48x)/90x+14=0
We multiply all the terms by the denominator
2x*90x+(-75x-105)+(-48x)+14*90x=0
Wy multiply elements
180x^2+(-75x-105)+(-48x)+1260x=0
We get rid of parentheses
180x^2-75x-48x+1260x-105=0
We add all the numbers together, and all the variables
180x^2+1137x-105=0
a = 180; b = 1137; c = -105;
Δ = b2-4ac
Δ = 11372-4·180·(-105)
Δ = 1368369
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1368369}=\sqrt{9*152041}=\sqrt{9}*\sqrt{152041}=3\sqrt{152041}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1137)-3\sqrt{152041}}{2*180}=\frac{-1137-3\sqrt{152041}}{360} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1137)+3\sqrt{152041}}{2*180}=\frac{-1137+3\sqrt{152041}}{360} $
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