(9x-13)(10x-19)=0

Solution for (9x-13)(10x-19)=0 equation:

(9x-13)(10x-19)=0

We multiply parentheses ..

(+90x^2-171x-130x+247)=0

We get rid of parentheses

90x^2-171x-130x+247=0

We add all the numbers together, and all the variables

90x^2-301x+247=0

a = 90; b = -301; c = +247;
Δ = b2-4ac
Δ = -3012-4·90·247
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-301)-41}{2*90}=\frac{260}{180}
=1+4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-301)+41}{2*90}=\frac{342}{180}
=1+9/10
$