1/2x+40=220-x

Solution for 1/2x+40=220-x equation:

1/2x+40=220-x

We move all terms to the left:

1/2x+40-(220-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1x+220)+40=0

We get rid of parentheses

1/2x+1x-220+40=0

We multiply all the terms by the denominator


1x*2x-220*2x+40*2x+1=0

Wy multiply elements

2x^2-440x+80x+1=0

We add all the numbers together, and all the variables

2x^2-360x+1=0

a = 2; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·2·1
Δ = 129592
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:

$\sqrt{\Delta}=\sqrt{129592}=\sqrt{4*32398}=\sqrt{4}*\sqrt{32398}=2\sqrt{32398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32398}}{2*2}=\frac{360-2\sqrt{32398}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32398}}{2*2}=\frac{360+2\sqrt{32398}}{4}
$