3x-6=4x(x-24)

Solution for 3x-6=4x(x-24) equation:

3x-6=4x(x-24)

We move all terms to the left:

3x-6-(4x(x-24))=0


We calculate terms in parentheses: -(4x(x-24)), so:

4x(x-24)

We multiply parentheses

4x^2-96x

Back to the equation:

-(4x^2-96x)


We get rid of parentheses

-4x^2+3x+96x-6=0

We add all the numbers together, and all the variables

-4x^2+99x-6=0

a = -4; b = 99; c = -6;
Δ = b2-4ac
Δ = 992-4·(-4)·(-6)
Δ = 9705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-\sqrt{9705}}{2*-4}=\frac{-99-\sqrt{9705}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+\sqrt{9705}}{2*-4}=\frac{-99+\sqrt{9705}}{-8}
$