1/2*x=45-x

Solution for 1/2*x=45-x equation:

1/2x=45-x

We move all terms to the left:

1/2x-(45-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+45)=0

We get rid of parentheses

1/2x+1x-45=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-90x+1=0

a = 2; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·2·1
Δ = 8092
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:

$\sqrt{\Delta}=\sqrt{8092}=\sqrt{1156*7}=\sqrt{1156}*\sqrt{7}=34\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-34\sqrt{7}}{2*2}=\frac{90-34\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+34\sqrt{7}}{2*2}=\frac{90+34\sqrt{7}}{4}
$