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(3-x)/(2x+5)=x/3
We move all terms to the left:
(3-x)/(2x+5)-(x/3)=0
Domain of the equation: (2x+5)!=0We add all the numbers together, and all the variables
We move all terms containing x to the left, all other terms to the right
2x!=-5
x!=-5/2
x!=-2+1/2
x∈R
(-1x+3)/(2x+5)-(+x/3)=0
We get rid of parentheses
(-1x+3)/(2x+5)-x/3=0
We calculate fractions
(-2x^2-5x)/(6x+15)+(-3x+9)/(6x+15)=0
We multiply all the terms by the denominator
(-2x^2-5x)+(-3x+9)=0
We get rid of parentheses
-2x^2-5x-3x+9=0
We add all the numbers together, and all the variables
-2x^2-8x+9=0
a = -2; b = -8; c = +9;
Δ = b2-4ac
Δ = -82-4·(-2)·9
Δ = 136
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*-2}=\frac{8-2\sqrt{34}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*-2}=\frac{8+2\sqrt{34}}{-4} $
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