0.3x(12x-16)=0.4(12-3x)

Solution for 0.3x(12x-16)=0.4(12-3x) equation:

0.3x(12x-16)=0.4(12-3x)

We move all terms to the left:

0.3x(12x-16)-(0.4(12-3x))=0

We add all the numbers together, and all the variables

0.3x(12x-16)-(0.4(-3x+12))=0

We multiply parentheses

0x^2+0x-(0.4(-3x+12))=0


We calculate terms in parentheses: -(0.4(-3x+12)), so:

0.4(-3x+12)

We multiply parentheses

-1.2x+4.8

Back to the equation:

-(-1.2x+4.8)


We add all the numbers together, and all the variables

x^2+x-(-1.2x+4.8)=0

We get rid of parentheses

x^2+x+1.2x-4.8=0

We add all the numbers together, and all the variables

x^2+2.2x-4.8=0

a = 1; b = 2.2; c = -4.8;
Δ = b2-4ac
Δ = 2.22-4·1·(-4.8)
Δ = 24.04
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{-(2.2)-\sqrt{24.04}}{2*1}=\frac{-2.2-\sqrt{24.04}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.2)+\sqrt{24.04}}{2*1}=\frac{-2.2+\sqrt{24.04}}{2}
$