1/3x+20=35+0.25x

Solution for 1/3x+20=35+0.25x equation:

1/3x+20=35+0.25x

We move all terms to the left:

1/3x+20-(35+0.25x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(0.25x+35)+20=0

We get rid of parentheses

1/3x-0.25x-35+20=0

We multiply all the terms by the denominator


-(0.25x)*3x-35*3x+20*3x+1=0

We add all the numbers together, and all the variables

-(+0.25x)*3x-35*3x+20*3x+1=0

We multiply parentheses

-0x^2-35*3x+20*3x+1=0

Wy multiply elements

-0x^2-105x+60x+1=0

We add all the numbers together, and all the variables

-1x^2-45x+1=0

a = -1; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·(-1)·1
Δ = 2029
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{-(-45)-\sqrt{2029}}{2*-1}=\frac{45-\sqrt{2029}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2029}}{2*-1}=\frac{45+\sqrt{2029}}{-2}
$