1.5x(x+3)=0.5(x-1)

Solution for 1.5x(x+3)=0.5(x-1) equation:

1.5x(x+3)=0.5(x-1)

We move all terms to the left:

1.5x(x+3)-(0.5(x-1))=0

We multiply parentheses

x^2+3x-(0.5(x-1))=0


We calculate terms in parentheses: -(0.5(x-1)), so:

0.5(x-1)

We multiply parentheses

0.5x-0.5

Back to the equation:

-(0.5x-0.5)


We get rid of parentheses

x^2+3x-0.5x+0.5=0

We add all the numbers together, and all the variables

x^2+2.5x+0.5=0

a = 1; b = 2.5; c = +0.5;
Δ = b2-4ac
Δ = 2.52-4·1·0.5
Δ = 4.25
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{-(2.5)-\sqrt{4.25}}{2*1}=\frac{-2.5-\sqrt{4.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{4.25}}{2*1}=\frac{-2.5+\sqrt{4.25}}{2}
$