6x(x+2)=5(1+x)

Solution for 6x(x+2)=5(1+x) equation:

6x(x+2)=5(1+x)

We move all terms to the left:

6x(x+2)-(5(1+x))=0

We add all the numbers together, and all the variables

6x(x+2)-(5(x+1))=0

We multiply parentheses

6x^2+12x-(5(x+1))=0


We calculate terms in parentheses: -(5(x+1)), so:

5(x+1)

We multiply parentheses

5x+5

Back to the equation:

-(5x+5)


We get rid of parentheses

6x^2+12x-5x-5=0

We add all the numbers together, and all the variables

6x^2+7x-5=0

a = 6; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·6·(-5)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*6}=\frac{6}{12}
=1/2
$