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

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

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

We move all terms to the left:

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

We multiply parentheses

6x-(7(7x-9)x)-6=0


We calculate terms in parentheses: -(7(7x-9)x), so:

7(7x-9)x

We multiply parentheses

49x^2-63x

Back to the equation:

-(49x^2-63x)


We get rid of parentheses

-49x^2+6x+63x-6=0

We add all the numbers together, and all the variables

-49x^2+69x-6=0

a = -49; b = 69; c = -6;
Δ = b2-4ac
Δ = 692-4·(-49)·(-6)
Δ = 3585
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{-(69)-\sqrt{3585}}{2*-49}=\frac{-69-\sqrt{3585}}{-98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{3585}}{2*-49}=\frac{-69+\sqrt{3585}}{-98}
$