(x-3)(23x-6)=0

Solution for (x-3)(23x-6)=0 equation:

(x-3)(23x-6)=0

We multiply parentheses ..

(+23x^2-6x-69x+18)=0

We get rid of parentheses

23x^2-6x-69x+18=0

We add all the numbers together, and all the variables

23x^2-75x+18=0

a = 23; b = -75; c = +18;
Δ = b2-4ac
Δ = -752-4·23·18
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-63}{2*23}=\frac{12}{46}
=6/23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+63}{2*23}=\frac{138}{46}
=3
$