(1/2x+24)+(3x-46)=86

Solution for (1/2x+24)+(3x-46)=86 equation:

(1/2x+24)+(3x-46)=86

We move all terms to the left:

(1/2x+24)+(3x-46)-(86)=0


Domain of the equation: 2x+24)!=0

x∈R


We get rid of parentheses

1/2x+3x+24-46-86=0

We multiply all the terms by the denominator


3x*2x+24*2x-46*2x-86*2x+1=0

Wy multiply elements

6x^2+48x-92x-172x+1=0

We add all the numbers together, and all the variables

6x^2-216x+1=0

a = 6; b = -216; c = +1;
Δ = b2-4ac
Δ = -2162-4·6·1
Δ = 46632
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:

$\sqrt{\Delta}=\sqrt{46632}=\sqrt{4*11658}=\sqrt{4}*\sqrt{11658}=2\sqrt{11658}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-2\sqrt{11658}}{2*6}=\frac{216-2\sqrt{11658}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+2\sqrt{11658}}{2*6}=\frac{216+2\sqrt{11658}}{12}
$