3.5x+-20+(1)/(2)x=40-2x

Solution for 3.5x+-20+(1)/(2)x=40-2x equation:

3.5x+-20+(1)/(2)x=40-2x

We move all terms to the left:

3.5x+-20+(1)/(2)x-(40-2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3.5x+1/2x-(-2x+40)-20+=0

We add all the numbers together, and all the variables

3.5x+1/2x-(-2x+40)=0

We get rid of parentheses

3.5x+1/2x+2x-40=0

We multiply all the terms by the denominator


(3.5x)*2x+2x*2x-40*2x+1=0

We add all the numbers together, and all the variables

(+3.5x)*2x+2x*2x-40*2x+1=0

We multiply parentheses

6x^2+2x*2x-40*2x+1=0

Wy multiply elements

6x^2+4x^2-80x+1=0

We add all the numbers together, and all the variables

10x^2-80x+1=0

a = 10; b = -80; c = +1;
Δ = b2-4ac
Δ = -802-4·10·1
Δ = 6360
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:

$\sqrt{\Delta}=\sqrt{6360}=\sqrt{4*1590}=\sqrt{4}*\sqrt{1590}=2\sqrt{1590}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1590}}{2*10}=\frac{80-2\sqrt{1590}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1590}}{2*10}=\frac{80+2\sqrt{1590}}{20}
$