(1/2x)+x=777

Solution for (1/2x)+x=777 equation:

(1/2x)+x=777

We move all terms to the left:

(1/2x)+x-(777)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2x)+x-777=0

We add all the numbers together, and all the variables

x+(+1/2x)-777=0

We get rid of parentheses

x+1/2x-777=0

We multiply all the terms by the denominator


x*2x-777*2x+1=0

Wy multiply elements

2x^2-1554x+1=0

a = 2; b = -1554; c = +1;
Δ = b2-4ac
Δ = -15542-4·2·1
Δ = 2414908
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:

$\sqrt{\Delta}=\sqrt{2414908}=\sqrt{4*603727}=\sqrt{4}*\sqrt{603727}=2\sqrt{603727}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1554)-2\sqrt{603727}}{2*2}=\frac{1554-2\sqrt{603727}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1554)+2\sqrt{603727}}{2*2}=\frac{1554+2\sqrt{603727}}{4}
$