0.4x(x-0.5)=0.2(x+3)

Solution for 0.4x(x-0.5)=0.2(x+3) equation:

0.4x(x-0.5)=0.2(x+3)

We move all terms to the left:

0.4x(x-0.5)-(0.2(x+3))=0

We multiply parentheses

0x^2-0x-(0.2(x+3))=0


We calculate terms in parentheses: -(0.2(x+3)), so:

0.2(x+3)

We multiply parentheses

0.2x+0.6

Back to the equation:

-(0.2x+0.6)


We add all the numbers together, and all the variables

x^2-1x-(0.2x+0.6)=0

We get rid of parentheses

x^2-1x-0.2x-0.6=0

We add all the numbers together, and all the variables

x^2-1.2x-0.6=0

a = 1; b = -1.2; c = -0.6;
Δ = b2-4ac
Δ = -1.22-4·1·(-0.6)
Δ = 3.84
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{-(-1.2)-\sqrt{3.84}}{2*1}=\frac{1.2-\sqrt{3.84}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.2)+\sqrt{3.84}}{2*1}=\frac{1.2+\sqrt{3.84}}{2}
$