1.5x^2=5.5x-2.1

Solution for 1.5x^2=5.5x-2.1 equation:

1.5x^2=5.5x-2.1

We move all terms to the left:

1.5x^2-(5.5x-2.1)=0

We get rid of parentheses

1.5x^2-5.5x+2.1=0

a = 1.5; b = -5.5; c = +2.1;
Δ = b2-4ac
Δ = -5.52-4·1.5·2.1
Δ = 17.65
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{-(-5.5)-\sqrt{17.65}}{2*1.5}=\frac{5.5-\sqrt{17.65}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{17.65}}{2*1.5}=\frac{5.5+\sqrt{17.65}}{3}
$