3x^2-4.5x-3=0

Solution for 3x^2-4.5x-3=0 equation:

3x^2-4.5x-3=0

a = 3; b = -4.5; c = -3;
Δ = b2-4ac
Δ = -4.52-4·3·(-3)
Δ = 56.25
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{56.25}}{2*3}=\frac{4.5-\sqrt{56.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{56.25}}{2*3}=\frac{4.5+\sqrt{56.25}}{6}
$