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

Solution for (x-6)(4x-3)=0 equation:

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

We multiply parentheses ..

(+4x^2-3x-24x+18)=0

We get rid of parentheses

4x^2-3x-24x+18=0

We add all the numbers together, and all the variables

4x^2-27x+18=0

a = 4; b = -27; c = +18;
Δ = b2-4ac
Δ = -272-4·4·18
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{-(-27)-21}{2*4}=\frac{6}{8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*4}=\frac{48}{8}
=6
$