(0.02-0.3X+x^2)=3.2(0.01+0.4x+4x^2)

Solution for (0.02-0.3X+x^2)=3.2(0.01+0.4x+4x^2) equation:

(0.02-0.3X+X^2)=3.2(0.01+0.4X+4X^2)

We move all terms to the left:

(0.02-0.3X+X^2)-(3.2(0.01+0.4X+4X^2))=0

We get rid of parentheses

X^2-(3.2(0.01+0.4X+4X^2))-0.3X+0.02=0


We calculate terms in parentheses: -(3.2(0.01+0.4X+4X^2)), so:

3.2(0.01+0.4X+4X^2)

We multiply parentheses

12.8X^2+0X+0.032

We add all the numbers together, and all the variables

12.8X^2+X+0.032

Back to the equation:

-(12.8X^2+X+0.032)


We add all the numbers together, and all the variables

X^2-0.3X-(12.8X^2+X+0.032)+0.02=0

We get rid of parentheses

X^2-12.8X^2-0.3X-X-0.032+0.02=0

We add all the numbers together, and all the variables

-11.8X^2-1.3X-0.012=0

a = -11.8; b = -1.3; c = -0.012;
Δ = b2-4ac
Δ = -1.32-4·(-11.8)·(-0.012)
Δ = 1.1236
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{-(-1.3)-\sqrt{1.1236}}{2*-11.8}=\frac{1.3-\sqrt{1.1236}}{-23.6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.3)+\sqrt{1.1236}}{2*-11.8}=\frac{1.3+\sqrt{1.1236}}{-23.6}
$