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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(13x(x+5)), so:

13x(x+5)

We multiply parentheses

13x^2+65x

Back to the equation:

-(13x^2+65x)


We get rid of parentheses

-13x^2+8x-65x+1=0

We add all the numbers together, and all the variables

-13x^2-57x+1=0

a = -13; b = -57; c = +1;
Δ = b2-4ac
Δ = -572-4·(-13)·1
Δ = 3301
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-\sqrt{3301}}{2*-13}=\frac{57-\sqrt{3301}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{3301}}{2*-13}=\frac{57+\sqrt{3301}}{-26}
$