(3x-1)*(x+3)=63

Solution for (3x-1)*(x+3)=63 equation:

(3x-1)(x+3)=63

We move all terms to the left:

(3x-1)(x+3)-(63)=0

We multiply parentheses ..

(+3x^2+9x-1x-3)-63=0

We get rid of parentheses

3x^2+9x-1x-3-63=0

We add all the numbers together, and all the variables

3x^2+8x-66=0

a = 3; b = 8; c = -66;
Δ = b2-4ac
Δ = 82-4·3·(-66)
Δ = 856
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:

$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{214}}{2*3}=\frac{-8-2\sqrt{214}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{214}}{2*3}=\frac{-8+2\sqrt{214}}{6}
$