(x+13)(3x+1)=90

Solution for (x+13)(3x+1)=90 equation:

(x+13)(3x+1)=90

We move all terms to the left:

(x+13)(3x+1)-(90)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+40x-77=0

a = 3; b = 40; c = -77;
Δ = b2-4ac
Δ = 402-4·3·(-77)
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{631}}{2*3}=\frac{-40-2\sqrt{631}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{631}}{2*3}=\frac{-40+2\sqrt{631}}{6}
$