1/2x=315-x

Solution for 1/2x=315-x equation:

1/2x=315-x

We move all terms to the left:

1/2x-(315-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+315)=0

We get rid of parentheses

1/2x+1x-315=0

We multiply all the terms by the denominator


1x*2x-315*2x+1=0

Wy multiply elements

2x^2-630x+1=0

a = 2; b = -630; c = +1;
Δ = b2-4ac
Δ = -6302-4·2·1
Δ = 396892
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:

$\sqrt{\Delta}=\sqrt{396892}=\sqrt{4*99223}=\sqrt{4}*\sqrt{99223}=2\sqrt{99223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99223}}{2*2}=\frac{630-2\sqrt{99223}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99223}}{2*2}=\frac{630+2\sqrt{99223}}{4}
$