3x^2-21x-23=100

Solution for 3x^2-21x-23=100 equation:

3x^2-21x-23=100

We move all terms to the left:

3x^2-21x-23-(100)=0

We add all the numbers together, and all the variables

3x^2-21x-123=0

a = 3; b = -21; c = -123;
Δ = b2-4ac
Δ = -212-4·3·(-123)
Δ = 1917
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:

$\sqrt{\Delta}=\sqrt{1917}=\sqrt{9*213}=\sqrt{9}*\sqrt{213}=3\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{213}}{2*3}=\frac{21-3\sqrt{213}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{213}}{2*3}=\frac{21+3\sqrt{213}}{6}
$