(8x+7)(x+1)=33

Solution for (8x+7)(x+1)=33 equation:

(8x+7)(x+1)=33

We move all terms to the left:

(8x+7)(x+1)-(33)=0

We multiply parentheses ..

(+8x^2+8x+7x+7)-33=0

We get rid of parentheses

8x^2+8x+7x+7-33=0

We add all the numbers together, and all the variables

8x^2+15x-26=0

a = 8; b = 15; c = -26;
Δ = b2-4ac
Δ = 152-4·8·(-26)
Δ = 1057
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{-(15)-\sqrt{1057}}{2*8}=\frac{-15-\sqrt{1057}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{1057}}{2*8}=\frac{-15+\sqrt{1057}}{16}
$