3.2(x+4)+2x2+1.7(x-3)=27

Solution for 3.2(x+4)+2x2+1.7(x-3)=27 equation:

3.2(x+4)+2x^2+1.7(x-3)=27

We move all terms to the left:

3.2(x+4)+2x^2+1.7(x-3)-(27)=0

We multiply parentheses

2x^2+3.2x+1.7x+12.8-5.1-27=0

We add all the numbers together, and all the variables

2x^2+4.9x-19.3=0

a = 2; b = 4.9; c = -19.3;
Δ = b2-4ac
Δ = 4.92-4·2·(-19.3)
Δ = 178.41
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{-(4.9)-\sqrt{178.41}}{2*2}=\frac{-4.9-\sqrt{178.41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.9)+\sqrt{178.41}}{2*2}=\frac{-4.9+\sqrt{178.41}}{4}
$