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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+3x^2+33x-7x-77)), so:

(+3x^2+33x-7x-77)

We get rid of parentheses

3x^2+33x-7x-77

We add all the numbers together, and all the variables

3x^2+26x-77

Back to the equation:

-(3x^2+26x-77)


We get rid of parentheses

-3x^2-26x+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}
$