(x-5)(3x+7)=21

Solution for (x-5)(3x+7)=21 equation:

(x-5)(3x+7)=21

We move all terms to the left:

(x-5)(3x+7)-(21)=0

We multiply parentheses ..

(+3x^2+7x-15x-35)-21=0

We get rid of parentheses

3x^2+7x-15x-35-21=0

We add all the numbers together, and all the variables

3x^2-8x-56=0

a = 3; b = -8; c = -56;
Δ = b2-4ac
Δ = -82-4·3·(-56)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{46}}{2*3}=\frac{8-4\sqrt{46}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{46}}{2*3}=\frac{8+4\sqrt{46}}{6}
$