1-3(x+3)=2(3x-4)9x

Solution for 1-3(x+3)=2(3x-4)9x equation:

1-3(x+3)=2(3x-4)9x

We move all terms to the left:

1-3(x+3)-(2(3x-4)9x)=0

We multiply parentheses

-3x-(2(3x-4)9x)-9+1=0


We calculate terms in parentheses: -(2(3x-4)9x), so:

2(3x-4)9x

We multiply parentheses

54x^2-72x

Back to the equation:

-(54x^2-72x)


We add all the numbers together, and all the variables

-3x-(54x^2-72x)-8=0

We get rid of parentheses

-54x^2-3x+72x-8=0

We add all the numbers together, and all the variables

-54x^2+69x-8=0

a = -54; b = 69; c = -8;
Δ = b2-4ac
Δ = 692-4·(-54)·(-8)
Δ = 3033
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:

$\sqrt{\Delta}=\sqrt{3033}=\sqrt{9*337}=\sqrt{9}*\sqrt{337}=3\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{337}}{2*-54}=\frac{-69-3\sqrt{337}}{-108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{337}}{2*-54}=\frac{-69+3\sqrt{337}}{-108}
$