1x=2/3x+5

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Solution for 1x=2/3x+5 equation:



1x=2/3x+5
We move all terms to the left:
1x-(2/3x+5)=0
Domain of the equation: 3x+5)!=0
x∈R
We add all the numbers together, and all the variables
x-(2/3x+5)=0
We get rid of parentheses
x-2/3x-5=0
We multiply all the terms by the denominator
x*3x-5*3x-2=0
Wy multiply elements
3x^2-15x-2=0
a = 3; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·3·(-2)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{249}}{2*3}=\frac{15-\sqrt{249}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{249}}{2*3}=\frac{15+\sqrt{249}}{6} $

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