0.3x(x-5)=0.2(6+x)

Solution for 0.3x(x-5)=0.2(6+x) equation:

0.3x(x-5)=0.2(6+x)

We move all terms to the left:

0.3x(x-5)-(0.2(6+x))=0

We add all the numbers together, and all the variables

0.3x(x-5)-(0.2(x+6))=0

We multiply parentheses

0x^2+0x-(0.2(x+6))=0


We calculate terms in parentheses: -(0.2(x+6)), so:

0.2(x+6)

We multiply parentheses

0.2x+1.2

Back to the equation:

-(0.2x+1.2)


We add all the numbers together, and all the variables

x^2+x-(0.2x+1.2)=0

We get rid of parentheses

x^2+x-0.2x-1.2=0

We add all the numbers together, and all the variables

x^2+0.8x-1.2=0

a = 1; b = 0.8; c = -1.2;
Δ = b2-4ac
Δ = 0.82-4·1·(-1.2)
Δ = 5.44
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{-(0.8)-\sqrt{5.44}}{2*1}=\frac{-0.8-\sqrt{5.44}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.8)+\sqrt{5.44}}{2*1}=\frac{-0.8+\sqrt{5.44}}{2}
$