1/2x+(x-6)=78

Solution for 1/2x+(x-6)=78 equation:

1/2x+(x-6)=78

We move all terms to the left:

1/2x+(x-6)-(78)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+x-6-78=0

We multiply all the terms by the denominator


x*2x-6*2x-78*2x+1=0

Wy multiply elements

2x^2-12x-156x+1=0

We add all the numbers together, and all the variables

2x^2-168x+1=0

a = 2; b = -168; c = +1;
Δ = b2-4ac
Δ = -1682-4·2·1
Δ = 28216
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:

$\sqrt{\Delta}=\sqrt{28216}=\sqrt{4*7054}=\sqrt{4}*\sqrt{7054}=2\sqrt{7054}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-2\sqrt{7054}}{2*2}=\frac{168-2\sqrt{7054}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+2\sqrt{7054}}{2*2}=\frac{168+2\sqrt{7054}}{4}
$