14=1/3x+5;x=18

Solution for 14=1/3x+5;x=18 equation:

14=1/3x+5x=18

We move all terms to the left:

14-(1/3x+5x)=0


Domain of the equation: 3x+5x)!=0

x∈R


We add all the numbers together, and all the variables

-(+5x+1/3x)+14=0

We get rid of parentheses

-5x-1/3x+14=0

We multiply all the terms by the denominator


-5x*3x+14*3x-1=0

Wy multiply elements

-15x^2+42x-1=0

a = -15; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·(-15)·(-1)
Δ = 1704
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:

$\sqrt{\Delta}=\sqrt{1704}=\sqrt{4*426}=\sqrt{4}*\sqrt{426}=2\sqrt{426}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{426}}{2*-15}=\frac{-42-2\sqrt{426}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{426}}{2*-15}=\frac{-42+2\sqrt{426}}{-30}
$