1,5x^2-4,5x=42

Solution for 1,5x^2-4,5x=42 equation:

1.5x^2-4.5x=42

We move all terms to the left:

1.5x^2-4.5x-(42)=0

a = 1.5; b = -4.5; c = -42;
Δ = b2-4ac
Δ = -4.52-4·1.5·(-42)
Δ = 272.25
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{-(-4.5)-\sqrt{272.25}}{2*1.5}=\frac{4.5-\sqrt{272.25}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{272.25}}{2*1.5}=\frac{4.5+\sqrt{272.25}}{3}
$