5.5x+x^2=42

Solution for 5.5x+x^2=42 equation:

5.5x+x^2=42

We move all terms to the left:

5.5x+x^2-(42)=0

a = 1; b = 5.5; c = -42;
Δ = b2-4ac
Δ = 5.52-4·1·(-42)
Δ = 198.25
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{-(5.5)-\sqrt{198.25}}{2*1}=\frac{-5.5-\sqrt{198.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.5)+\sqrt{198.25}}{2*1}=\frac{-5.5+\sqrt{198.25}}{2}
$