(13x+3)(x+3)=90

Solution for (13x+3)(x+3)=90 equation:

(13x+3)(x+3)=90

We move all terms to the left:

(13x+3)(x+3)-(90)=0

We multiply parentheses ..

(+13x^2+39x+3x+9)-90=0

We get rid of parentheses

13x^2+39x+3x+9-90=0

We add all the numbers together, and all the variables

13x^2+42x-81=0

a = 13; b = 42; c = -81;
Δ = b2-4ac
Δ = 422-4·13·(-81)
Δ = 5976
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:

$\sqrt{\Delta}=\sqrt{5976}=\sqrt{36*166}=\sqrt{36}*\sqrt{166}=6\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{166}}{2*13}=\frac{-42-6\sqrt{166}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{166}}{2*13}=\frac{-42+6\sqrt{166}}{26}
$