24(x-2)(2x-7)/6(2x-7)(x+6)=0

Solution for 24(x-2)(2x-7)/6(2x-7)(x+6)=0 equation:

24(x-2)(2x-7)/6(2x-7)(x+6)=0


Domain of the equation: 6(2x-7)(x+6)!=0

x∈R


We multiply parentheses ..

24(+2x^2-7x-4x+14)/6(2x-7)(x+6)=0

We multiply all the terms by the denominator


24(+2x^2-7x-4x+14)=0

We multiply parentheses

48x^2-168x-96x+336=0

We add all the numbers together, and all the variables

48x^2-264x+336=0

a = 48; b = -264; c = +336;
Δ = b2-4ac
Δ = -2642-4·48·336
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-72}{2*48}=\frac{192}{96}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+72}{2*48}=\frac{336}{96}
=3+1/2
$