(x-2)(3x-7)=24

Solution for (x-2)(3x-7)=24 equation:

(x-2)(3x-7)=24

We move all terms to the left:

(x-2)(3x-7)-(24)=0

We multiply parentheses ..

(+3x^2-7x-6x+14)-24=0

We get rid of parentheses

3x^2-7x-6x+14-24=0

We add all the numbers together, and all the variables

3x^2-13x-10=0

a = 3; b = -13; c = -10;
Δ = b2-4ac
Δ = -132-4·3·(-10)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*3}=\frac{-4}{6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*3}=\frac{30}{6}
=5
$