(3x-7)(x+11)=588

Solution for (3x-7)(x+11)=588 equation:

(3x-7)(x+11)=588

We move all terms to the left:

(3x-7)(x+11)-(588)=0

We multiply parentheses ..

(+3x^2+33x-7x-77)-588=0

We get rid of parentheses

3x^2+33x-7x-77-588=0

We add all the numbers together, and all the variables

3x^2+26x-665=0

a = 3; b = 26; c = -665;
Δ = b2-4ac
Δ = 262-4·3·(-665)
Δ = 8656
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:

$\sqrt{\Delta}=\sqrt{8656}=\sqrt{16*541}=\sqrt{16}*\sqrt{541}=4\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-4\sqrt{541}}{2*3}=\frac{-26-4\sqrt{541}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+4\sqrt{541}}{2*3}=\frac{-26+4\sqrt{541}}{6}
$