3(x+6)=1/2x-7

Solution for 3(x+6)=1/2x-7 equation:

3(x+6)=1/2x-7

We move all terms to the left:

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


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

x∈R


We multiply parentheses

3x-(1/2x-7)+18=0

We get rid of parentheses

3x-1/2x+7+18=0

We multiply all the terms by the denominator


3x*2x+7*2x+18*2x-1=0

Wy multiply elements

6x^2+14x+36x-1=0

We add all the numbers together, and all the variables

6x^2+50x-1=0

a = 6; b = 50; c = -1;
Δ = b2-4ac
Δ = 502-4·6·(-1)
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{631}}{2*6}=\frac{-50-2\sqrt{631}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{631}}{2*6}=\frac{-50+2\sqrt{631}}{12}
$