8x=1/2*18x-12

Solution for 8x=1/2*18x-12 equation:

8x=1/2*18x-12

We move all terms to the left:

8x-(1/2*18x-12)=0


Domain of the equation: 2*18x-12)!=0

x∈R


We get rid of parentheses

8x-1/2*18x+12=0

We multiply all the terms by the denominator


8x*2*18x+12*2*18x-1=0

Wy multiply elements

288x^2*1+432x*1-1=0

Wy multiply elements

288x^2+432x-1=0

a = 288; b = 432; c = -1;
Δ = b2-4ac
Δ = 4322-4·288·(-1)
Δ = 187776
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:

$\sqrt{\Delta}=\sqrt{187776}=\sqrt{576*326}=\sqrt{576}*\sqrt{326}=24\sqrt{326}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(432)-24\sqrt{326}}{2*288}=\frac{-432-24\sqrt{326}}{576}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(432)+24\sqrt{326}}{2*288}=\frac{-432+24\sqrt{326}}{576}
$