2.25-4.5x-4x^2=0

Solution for 2.25-4.5x-4x^2=0 equation:

2.25-4.5x-4x^2=0

a = -4; b = -4.5; c = +2.25;
Δ = b2-4ac
Δ = -4.52-4·(-4)·2.25
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*-4}=\frac{4.5-\sqrt{56.25}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.5)+\sqrt{56.25}}{2*-4}=\frac{4.5+\sqrt{56.25}}{-8}
$