3x(7x-9)=9x-8(2x-1)

Solution for 3x(7x-9)=9x-8(2x-1) equation:

3x(7x-9)=9x-8(2x-1)

We move all terms to the left:

3x(7x-9)-(9x-8(2x-1))=0

We multiply parentheses

21x^2-27x-(9x-8(2x-1))=0


We calculate terms in parentheses: -(9x-8(2x-1)), so:

9x-8(2x-1)

We multiply parentheses

9x-16x+8

We add all the numbers together, and all the variables

-7x+8

Back to the equation:

-(-7x+8)


We get rid of parentheses

21x^2-27x+7x-8=0

We add all the numbers together, and all the variables

21x^2-20x-8=0

a = 21; b = -20; c = -8;
Δ = b2-4ac
Δ = -202-4·21·(-8)
Δ = 1072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{67}}{2*21}=\frac{20-4\sqrt{67}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{67}}{2*21}=\frac{20+4\sqrt{67}}{42}
$