8x(2x-4)=3(x-6)

Solution for 8x(2x-4)=3(x-6) equation:

8x(2x-4)=3(x-6)

We move all terms to the left:

8x(2x-4)-(3(x-6))=0

We multiply parentheses

16x^2-32x-(3(x-6))=0


We calculate terms in parentheses: -(3(x-6)), so:

3(x-6)

We multiply parentheses

3x-18

Back to the equation:

-(3x-18)


We get rid of parentheses

16x^2-32x-3x+18=0

We add all the numbers together, and all the variables

16x^2-35x+18=0

a = 16; b = -35; c = +18;
Δ = b2-4ac
Δ = -352-4·16·18
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{73}}{2*16}=\frac{35-\sqrt{73}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{73}}{2*16}=\frac{35+\sqrt{73}}{32}
$