1/2x+x=78

Solution for 1/2x+x=78 equation:

1/2x+x=78

We move all terms to the left:

1/2x+x-(78)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-78=0

We multiply all the terms by the denominator


x*2x-78*2x+1=0

Wy multiply elements

2x^2-156x+1=0

a = 2; b = -156; c = +1;
Δ = b2-4ac
Δ = -1562-4·2·1
Δ = 24328
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:

$\sqrt{\Delta}=\sqrt{24328}=\sqrt{4*6082}=\sqrt{4}*\sqrt{6082}=2\sqrt{6082}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-2\sqrt{6082}}{2*2}=\frac{156-2\sqrt{6082}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+2\sqrt{6082}}{2*2}=\frac{156+2\sqrt{6082}}{4}
$