x(5x+8)=13

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

x(5x+8)=13

We move all terms to the left:

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

We multiply parentheses

5x^2+8x-13=0

a = 5; b = 8; c = -13;
Δ = b2-4ac
Δ = 82-4·5·(-13)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-18}{2*5}=\frac{-26}{10}
=-2+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+18}{2*5}=\frac{10}{10}
=1
$