(3.5x+3)=(x^2+5.5x)

Solution for (3.5x+3)=(x^2+5.5x) equation:

(3.5x+3)=(x^2+5.5x)

We move all terms to the left:

(3.5x+3)-((x^2+5.5x))=0

We get rid of parentheses

3.5x-((x^2+5.5x))+3=0


We calculate terms in parentheses: -((x^2+5.5x)), so:

(x^2+5.5x)

We get rid of parentheses

x^2+5.5x

Back to the equation:

-(x^2+5.5x)


We get rid of parentheses

-x^2+3.5x-5.5x+3=0

We add all the numbers together, and all the variables

-1x^2-2x+3=0

a = -1; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-1)·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*-1}=\frac{6}{-2}
=-3
$