(X-4)(9x-1)=0

Solution for (X-4)(9x-1)=0 equation:

(X-4)(9X-1)=0

We multiply parentheses ..

(+9X^2-1X-36X+4)=0

We get rid of parentheses

9X^2-1X-36X+4=0

We add all the numbers together, and all the variables

9X^2-37X+4=0

a = 9; b = -37; c = +4;
Δ = b2-4ac
Δ = -372-4·9·4
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-35}{2*9}=\frac{2}{18}
=1/9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+35}{2*9}=\frac{72}{18}
=4
$