(8x-9)x+x+6=3(x+1)

Solution for (8x-9)x+x+6=3(x+1) equation:

(8x-9)x+x+6=3(x+1)

We move all terms to the left:

(8x-9)x+x+6-(3(x+1))=0

We add all the numbers together, and all the variables

x+(8x-9)x-(3(x+1))+6=0

We multiply parentheses

8x^2+x-9x-(3(x+1))+6=0


We calculate terms in parentheses: -(3(x+1)), so:

3(x+1)

We multiply parentheses

3x+3

Back to the equation:

-(3x+3)


We add all the numbers together, and all the variables

8x^2-8x-(3x+3)+6=0

We get rid of parentheses

8x^2-8x-3x-3+6=0

We add all the numbers together, and all the variables

8x^2-11x+3=0

a = 8; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·8·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*8}=\frac{6}{16}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*8}=\frac{16}{16}
=1
$