10+x=5(1/3x+2)

Solution for 10+x=5(1/3x+2) equation:

10+x=5(1/3x+2)

We move all terms to the left:

10+x-(5(1/3x+2))=0


Domain of the equation: 3x+2))!=0

x∈R


We multiply all the terms by the denominator


x*3x+10*3x+2))-(5(1+2))=0

We add all the numbers together, and all the variables

x*3x+10*3x+2))-(53)=0

We add all the numbers together, and all the variables

x*3x+10*3x=0

Wy multiply elements

3x^2+30x=0

a = 3; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·3·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*3}=\frac{-60}{6}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*3}=\frac{0}{6}
=0
$