(19x-1)(13x-5)=90

Solution for (19x-1)(13x-5)=90 equation:

(19x-1)(13x-5)=90

We move all terms to the left:

(19x-1)(13x-5)-(90)=0

We multiply parentheses ..

(+247x^2-95x-13x+5)-90=0

We get rid of parentheses

247x^2-95x-13x+5-90=0

We add all the numbers together, and all the variables

247x^2-108x-85=0

a = 247; b = -108; c = -85;
Δ = b2-4ac
Δ = -1082-4·247·(-85)
Δ = 95644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{95644}=\sqrt{4*23911}=\sqrt{4}*\sqrt{23911}=2\sqrt{23911}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{23911}}{2*247}=\frac{108-2\sqrt{23911}}{494}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{23911}}{2*247}=\frac{108+2\sqrt{23911}}{494}
$