7x(x-6)=3x+9

Solution for 7x(x-6)=3x+9 equation:

7x(x-6)=3x+9

We move all terms to the left:

7x(x-6)-(3x+9)=0

We multiply parentheses

7x^2-42x-(3x+9)=0

We get rid of parentheses

7x^2-42x-3x-9=0

We add all the numbers together, and all the variables

7x^2-45x-9=0

a = 7; b = -45; c = -9;
Δ = b2-4ac
Δ = -452-4·7·(-9)
Δ = 2277
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:

$\sqrt{\Delta}=\sqrt{2277}=\sqrt{9*253}=\sqrt{9}*\sqrt{253}=3\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{253}}{2*7}=\frac{45-3\sqrt{253}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{253}}{2*7}=\frac{45+3\sqrt{253}}{14}
$