(x^2+4x+-4.5)=0

Solution for (x^2+4x+-4.5)=0 equation:

(x^2+4x+-4.5)=0

We use the square of the difference formula

(x^2+4x-4.5)=0

We get rid of parentheses

x^2+4x-4.5=0

a = 1; b = 4; c = -4.5;
Δ = b2-4ac
Δ = 42-4·1·(-4.5)
Δ = 34
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)-\sqrt{34}}{2*1}=\frac{-4-\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{34}}{2*1}=\frac{-4+\sqrt{34}}{2}
$