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2/3x-5x=26
We move all terms to the left:
2/3x-5x-(26)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-5x+2/3x-26=0
We multiply all the terms by the denominator
-5x*3x-26*3x+2=0
Wy multiply elements
-15x^2-78x+2=0
a = -15; b = -78; c = +2;
Δ = b2-4ac
Δ = -782-4·(-15)·2
Δ = 6204
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6204}=\sqrt{4*1551}=\sqrt{4}*\sqrt{1551}=2\sqrt{1551}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1551}}{2*-15}=\frac{78-2\sqrt{1551}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1551}}{2*-15}=\frac{78+2\sqrt{1551}}{-30} $
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