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

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

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

We move all terms to the left:

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

We multiply parentheses

-4x^2+8x-((3x-8))=0


We calculate terms in parentheses: -((3x-8)), so:

(3x-8)

We get rid of parentheses

3x-8

Back to the equation:

-(3x-8)


We get rid of parentheses

-4x^2+8x-3x+8=0

We add all the numbers together, and all the variables

-4x^2+5x+8=0

a = -4; b = 5; c = +8;
Δ = b2-4ac
Δ = 52-4·(-4)·8
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{17}}{2*-4}=\frac{-5-3\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{17}}{2*-4}=\frac{-5+3\sqrt{17}}{-8}
$