x+(1/2x-4)=35

Solution for x+(1/2x-4)=35 equation:

x+(1/2x-4)=35

We move all terms to the left:

x+(1/2x-4)-(35)=0


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

x+1/2x-4-35=0

We multiply all the terms by the denominator


x*2x-4*2x-35*2x+1=0

Wy multiply elements

2x^2-8x-70x+1=0

We add all the numbers together, and all the variables

2x^2-78x+1=0

a = 2; b = -78; c = +1;
Δ = b2-4ac
Δ = -782-4·2·1
Δ = 6076
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:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-14\sqrt{31}}{2*2}=\frac{78-14\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+14\sqrt{31}}{2*2}=\frac{78+14\sqrt{31}}{4}
$