(3x+27)(x+7)=969

Solution for (3x+27)(x+7)=969 equation:

(3x+27)(x+7)=969

We move all terms to the left:

(3x+27)(x+7)-(969)=0

We multiply parentheses ..

(+3x^2+21x+27x+189)-969=0

We get rid of parentheses

3x^2+21x+27x+189-969=0

We add all the numbers together, and all the variables

3x^2+48x-780=0

a = 3; b = 48; c = -780;
Δ = b2-4ac
Δ = 482-4·3·(-780)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-108}{2*3}=\frac{-156}{6}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+108}{2*3}=\frac{60}{6}
=10
$