20+(2/3x)=15+8x

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Solution for 20+(2/3x)=15+8x equation:



20+(2/3x)=15+8x
We move all terms to the left:
20+(2/3x)-(15+8x)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+2/3x)-(8x+15)+20=0
We get rid of parentheses
2/3x-8x-15+20=0
We multiply all the terms by the denominator
-8x*3x-15*3x+20*3x+2=0
Wy multiply elements
-24x^2-45x+60x+2=0
We add all the numbers together, and all the variables
-24x^2+15x+2=0
a = -24; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-24)·2
Δ = 417
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{417}}{2*-24}=\frac{-15-\sqrt{417}}{-48} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{417}}{2*-24}=\frac{-15+\sqrt{417}}{-48} $

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