0.6x(x+2)=0.55(2x+3)

Solution for 0.6x(x+2)=0.55(2x+3) equation:

0.6x(x+2)=0.55(2x+3)

We move all terms to the left:

0.6x(x+2)-(0.55(2x+3))=0

We multiply parentheses

0x^2+0x-(0.55(2x+3))=0


We calculate terms in parentheses: -(0.55(2x+3)), so:

0.55(2x+3)

We multiply parentheses

1.1x+1.65

Back to the equation:

-(1.1x+1.65)


We add all the numbers together, and all the variables

x^2+x-(1.1x+1.65)=0

We get rid of parentheses

x^2+x-1.1x-1.65=0

We add all the numbers together, and all the variables

x^2-0.1x-1.65=0

a = 1; b = -0.1; c = -1.65;
Δ = b2-4ac
Δ = -0.12-4·1·(-1.65)
Δ = 6.61
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{-(-0.1)-\sqrt{6.61}}{2*1}=\frac{0.1-\sqrt{6.61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{6.61}}{2*1}=\frac{0.1+\sqrt{6.61}}{2}
$