4x(x-2)=3(1.5+x)

Solution for 4x(x-2)=3(1.5+x) equation:

4x(x-2)=3(1.5+x)

We move all terms to the left:

4x(x-2)-(3(1.5+x))=0

We add all the numbers together, and all the variables

4x(x-2)-(3(x+1.5))=0

We multiply parentheses

4x^2-8x-(3(x+1.5))=0


We calculate terms in parentheses: -(3(x+1.5)), so:

3(x+1.5)

We multiply parentheses

3x+4.5

Back to the equation:

-(3x+4.5)


We get rid of parentheses

4x^2-8x-3x-4.5=0

We add all the numbers together, and all the variables

4x^2-11x-4.5=0

a = 4; b = -11; c = -4.5;
Δ = b2-4ac
Δ = -112-4·4·(-4.5)
Δ = 193
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{-(-11)-\sqrt{193}}{2*4}=\frac{11-\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{193}}{2*4}=\frac{11+\sqrt{193}}{8}
$