X+(X+34)(3x-33)=966

Solution for X+(X+34)(3x-33)=966 equation:

X+(X+34)(3X-33)=966

We move all terms to the left:

X+(X+34)(3X-33)-(966)=0

We multiply parentheses ..

(+3X^2-33X+102X-1122)+X-966=0

We get rid of parentheses

3X^2-33X+102X+X-1122-966=0

We add all the numbers together, and all the variables

3X^2+70X-2088=0

a = 3; b = 70; c = -2088;
Δ = b2-4ac
Δ = 702-4·3·(-2088)
Δ = 29956
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:

$\sqrt{\Delta}=\sqrt{29956}=\sqrt{4*7489}=\sqrt{4}*\sqrt{7489}=2\sqrt{7489}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{7489}}{2*3}=\frac{-70-2\sqrt{7489}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{7489}}{2*3}=\frac{-70+2\sqrt{7489}}{6}
$