(x-9)(4x-19)=0

Solution for (x-9)(4x-19)=0 equation:

(x-9)(4x-19)=0

We multiply parentheses ..

(+4x^2-19x-36x+171)=0

We get rid of parentheses

4x^2-19x-36x+171=0

We add all the numbers together, and all the variables

4x^2-55x+171=0

a = 4; b = -55; c = +171;
Δ = b2-4ac
Δ = -552-4·4·171
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-17}{2*4}=\frac{38}{8}
=4+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+17}{2*4}=\frac{72}{8}
=9
$