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

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



3.5x+-20+1/2x=40-2x
We move all terms to the left:
3.5x+-20+1/2x-(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} $

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