(13x+1)(7x+19)=90

Solution for (13x+1)(7x+19)=90 equation:

(13x+1)(7x+19)=90

We move all terms to the left:

(13x+1)(7x+19)-(90)=0

We multiply parentheses ..

(+91x^2+247x+7x+19)-90=0

We get rid of parentheses

91x^2+247x+7x+19-90=0

We add all the numbers together, and all the variables

91x^2+254x-71=0

a = 91; b = 254; c = -71;
Δ = b2-4ac
Δ = 2542-4·91·(-71)
Δ = 90360
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:

$\sqrt{\Delta}=\sqrt{90360}=\sqrt{36*2510}=\sqrt{36}*\sqrt{2510}=6\sqrt{2510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(254)-6\sqrt{2510}}{2*91}=\frac{-254-6\sqrt{2510}}{182}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(254)+6\sqrt{2510}}{2*91}=\frac{-254+6\sqrt{2510}}{182}
$