x-6=3x^2-14x-24

Solution for x-6=3x^2-14x-24 equation:

x-6=3x^2-14x-24

We move all terms to the left:

x-6-(3x^2-14x-24)=0

We get rid of parentheses

-3x^2+x+14x+24-6=0

We add all the numbers together, and all the variables

-3x^2+15x+18=0

a = -3; b = 15; c = +18;
Δ = b2-4ac
Δ = 152-4·(-3)·18
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*-3}=\frac{6}{-6}
=-1
$