6x=1/2x+7+59

Solution for 6x=1/2x+7+59 equation:

6x=1/2x+7+59

We move all terms to the left:

6x-(1/2x+7+59)=0


Domain of the equation: 2x+7+59)!=0

We move all terms containing x to the left, all other terms to the right

2x+59)!=-7

x∈R


We add all the numbers together, and all the variables

6x-(1/2x+66)=0

We get rid of parentheses

6x-1/2x-66=0

We multiply all the terms by the denominator


6x*2x-66*2x-1=0

Wy multiply elements

12x^2-132x-1=0

a = 12; b = -132; c = -1;
Δ = b2-4ac
Δ = -1322-4·12·(-1)
Δ = 17472
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:

$\sqrt{\Delta}=\sqrt{17472}=\sqrt{64*273}=\sqrt{64}*\sqrt{273}=8\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-8\sqrt{273}}{2*12}=\frac{132-8\sqrt{273}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+8\sqrt{273}}{2*12}=\frac{132+8\sqrt{273}}{24}
$