3*x-9=1/4*16x-8

Solution for 3*x-9=1/4*16x-8 equation:

3x-9=1/4*16x-8

We move all terms to the left:

3x-9-(1/4*16x-8)=0


Domain of the equation: 4*16x-8)!=0

x∈R


We get rid of parentheses

3x-1/4*16x+8-9=0

We multiply all the terms by the denominator


3x*4*16x+8*4*16x-9*4*16x-1=0

Wy multiply elements

192x^2*1+512x*1-576x*1-1=0

Wy multiply elements

192x^2+512x-576x-1=0

We add all the numbers together, and all the variables

192x^2-64x-1=0

a = 192; b = -64; c = -1;
Δ = b2-4ac
Δ = -642-4·192·(-1)
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{19}}{2*192}=\frac{64-16\sqrt{19}}{384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{19}}{2*192}=\frac{64+16\sqrt{19}}{384}
$