(3x+7)(x-13)=-16

Solution for (3x+7)(x-13)=-16 equation:

(3x+7)(x-13)=-16

We move all terms to the left:

(3x+7)(x-13)-(-16)=0

We add all the numbers together, and all the variables

(3x+7)(x-13)+16=0

We multiply parentheses ..

(+3x^2-39x+7x-91)+16=0

We get rid of parentheses

3x^2-39x+7x-91+16=0

We add all the numbers together, and all the variables

3x^2-32x-75=0

a = 3; b = -32; c = -75;
Δ = b2-4ac
Δ = -322-4·3·(-75)
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{481}}{2*3}=\frac{32-2\sqrt{481}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{481}}{2*3}=\frac{32+2\sqrt{481}}{6}
$