(5x-4)(x-6)(3)=600

Solution for (5x-4)(x-6)(3)=600 equation:

(5x-4)(x-6)(3)=600

We move all terms to the left:

(5x-4)(x-6)(3)-(600)=0

We multiply parentheses ..

(+5x^2-30x-4x+24)3-600=0

We multiply parentheses

15x^2-90x-12x+72-600=0

We add all the numbers together, and all the variables

15x^2-102x-528=0

a = 15; b = -102; c = -528;
Δ = b2-4ac
Δ = -1022-4·15·(-528)
Δ = 42084
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:

$\sqrt{\Delta}=\sqrt{42084}=\sqrt{36*1169}=\sqrt{36}*\sqrt{1169}=6\sqrt{1169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-6\sqrt{1169}}{2*15}=\frac{102-6\sqrt{1169}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+6\sqrt{1169}}{2*15}=\frac{102+6\sqrt{1169}}{30}
$