7x(3x-9)=5x-4x+2

Solution for 7x(3x-9)=5x-4x+2 equation:

7x(3x-9)=5x-4x+2

We move all terms to the left:

7x(3x-9)-(5x-4x+2)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

21x^2-63x-(x+2)=0

We get rid of parentheses

21x^2-63x-x-2=0

We add all the numbers together, and all the variables

21x^2-64x-2=0

a = 21; b = -64; c = -2;
Δ = b2-4ac
Δ = -642-4·21·(-2)
Δ = 4264
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:

$\sqrt{\Delta}=\sqrt{4264}=\sqrt{4*1066}=\sqrt{4}*\sqrt{1066}=2\sqrt{1066}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{1066}}{2*21}=\frac{64-2\sqrt{1066}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{1066}}{2*21}=\frac{64+2\sqrt{1066}}{42}
$