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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+16x^2-32x+6x-12)-((4x-6)*2)=0


We calculate terms in parentheses: -((4x-6)*2), so:

(4x-6)*2

We multiply parentheses

8x-12

Back to the equation:

-(8x-12)


We get rid of parentheses

16x^2-32x+6x-8x-12+12=0

We add all the numbers together, and all the variables

16x^2-34x=0

a = 16; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·16·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*16}=\frac{68}{32}
=2+1/8
$