1/2x+6(x+15)=12

Solution for 1/2x+6(x+15)=12 equation:

1/2x+6(x+15)=12

We move all terms to the left:

1/2x+6(x+15)-(12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

1/2x+6x+90-12=0

We multiply all the terms by the denominator


6x*2x+90*2x-12*2x+1=0

Wy multiply elements

12x^2+180x-24x+1=0

We add all the numbers together, and all the variables

12x^2+156x+1=0

a = 12; b = 156; c = +1;
Δ = b2-4ac
Δ = 1562-4·12·1
Δ = 24288
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:

$\sqrt{\Delta}=\sqrt{24288}=\sqrt{16*1518}=\sqrt{16}*\sqrt{1518}=4\sqrt{1518}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-4\sqrt{1518}}{2*12}=\frac{-156-4\sqrt{1518}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+4\sqrt{1518}}{2*12}=\frac{-156+4\sqrt{1518}}{24}
$