x^2+x=3.2/4.4

Solution for x^2+x=3.2/4.4 equation:

x^2+x=3.2/4.4

We move all terms to the left:

x^2+x-(3.2/4.4)=0

We add all the numbers together, and all the variables

x^2+x-(+3.2/4.4)=0

We get rid of parentheses

x^2+x-3.2/4.4=0

We multiply all the terms by the denominator


x^2*4.4+x*4.4-3.2=0

Wy multiply elements

4.4x^2+4.4x-3.2=0

a = 4.4; b = 4.4; c = -3.2;
Δ = b2-4ac
Δ = 4.42-4·4.4·(-3.2)
Δ = 75.68
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{-(4.4)-\sqrt{75.68}}{2*4.4}=\frac{-4.4-\sqrt{75.68}}{8.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.4)+\sqrt{75.68}}{2*4.4}=\frac{-4.4+\sqrt{75.68}}{8.8}
$