(5x+1)(13x-8)=198

Solution for (5x+1)(13x-8)=198 equation:

(5x+1)(13x-8)=198

We move all terms to the left:

(5x+1)(13x-8)-(198)=0

We multiply parentheses ..

(+65x^2-40x+13x-8)-198=0

We get rid of parentheses

65x^2-40x+13x-8-198=0

We add all the numbers together, and all the variables

65x^2-27x-206=0

a = 65; b = -27; c = -206;
Δ = b2-4ac
Δ = -272-4·65·(-206)
Δ = 54289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54289}=233$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-233}{2*65}=\frac{-206}{130}
=-1+38/65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+233}{2*65}=\frac{260}{130}
=2
$