20=7/3x+x

Solution for 20=7/3x+x equation:

20=7/3x+x

We move all terms to the left:

20-(7/3x+x)=0


Domain of the equation: 3x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+7/3x)+20=0

We get rid of parentheses

-x-7/3x+20=0

We multiply all the terms by the denominator


-x*3x+20*3x-7=0

Wy multiply elements

-3x^2+60x-7=0

a = -3; b = 60; c = -7;
Δ = b2-4ac
Δ = 602-4·(-3)·(-7)
Δ = 3516
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:

$\sqrt{\Delta}=\sqrt{3516}=\sqrt{4*879}=\sqrt{4}*\sqrt{879}=2\sqrt{879}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{879}}{2*-3}=\frac{-60-2\sqrt{879}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{879}}{2*-3}=\frac{-60+2\sqrt{879}}{-6}
$