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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3(x+2)-4), so:

3(x+2)-4

We multiply parentheses

3x+6-4

We add all the numbers together, and all the variables

3x+2

Back to the equation:

-(3x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-11x-2=0

a = 4; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·4·(-2)
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{-(-11)-3\sqrt{17}}{2*4}=\frac{11-3\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{17}}{2*4}=\frac{11+3\sqrt{17}}{8}
$