3(x+4)=1/2x-5

Solution for 3(x+4)=1/2x-5 equation:

3(x+4)=1/2x-5

We move all terms to the left:

3(x+4)-(1/2x-5)=0


Domain of the equation: 2x-5)!=0

x∈R


We multiply parentheses

3x-(1/2x-5)+12=0

We get rid of parentheses

3x-1/2x+5+12=0

We multiply all the terms by the denominator


3x*2x+5*2x+12*2x-1=0

Wy multiply elements

6x^2+10x+24x-1=0

We add all the numbers together, and all the variables

6x^2+34x-1=0

a = 6; b = 34; c = -1;
Δ = b2-4ac
Δ = 342-4·6·(-1)
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{295}}{2*6}=\frac{-34-2\sqrt{295}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{295}}{2*6}=\frac{-34+2\sqrt{295}}{12}
$