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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


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

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

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 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}
$