3(x+9)=-1/2x+2

Solution for 3(x+9)=-1/2x+2 equation:

3(x+9)=-1/2x+2

We move all terms to the left:

3(x+9)-(-1/2x+2)=0


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

x∈R


We multiply parentheses

3x-(-1/2x+2)+27=0

We get rid of parentheses

3x+1/2x-2+27=0

We multiply all the terms by the denominator


3x*2x-2*2x+27*2x+1=0

Wy multiply elements

6x^2-4x+54x+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 = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{619}}{2*6}=\frac{-50-2\sqrt{619}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{619}}{2*6}=\frac{-50+2\sqrt{619}}{12}
$