0.12(24)+0.02x=0.4x(12+x)

Solution for 0.12(24)+0.02x=0.4x(12+x) equation:

0.12(24)+0.02x=0.4x(12+x)

We move all terms to the left:

0.12(24)+0.02x-(0.4x(12+x))=0

We add all the numbers together, and all the variables

0.02x-(0.4x(x+12))+0.1224=0


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

0.4x(x+12)

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2+0.02x-x+0.1224=0

We add all the numbers together, and all the variables

-1x^2-0.98x+0.1224=0

a = -1; b = -0.98; c = +0.1224;
Δ = b2-4ac
Δ = -0.982-4·(-1)·0.1224
Δ = 1.45
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{-(-0.98)-\sqrt{1.45}}{2*-1}=\frac{0.98-\sqrt{1.45}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.98)+\sqrt{1.45}}{2*-1}=\frac{0.98+\sqrt{1.45}}{-2}
$