(8x+3)(x+1)=13

Solution for (8x+3)(x+1)=13 equation:

(8x+3)(x+1)=13

We move all terms to the left:

(8x+3)(x+1)-(13)=0

We multiply parentheses ..

(+8x^2+8x+3x+3)-13=0

We get rid of parentheses

8x^2+8x+3x+3-13=0

We add all the numbers together, and all the variables

8x^2+11x-10=0

a = 8; b = 11; c = -10;
Δ = b2-4ac
Δ = 112-4·8·(-10)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*8}=\frac{10}{16}
=5/8
$