(x+8)(8x+1)=90

Solution for (x+8)(8x+1)=90 equation:

(x+8)(8x+1)=90

We move all terms to the left:

(x+8)(8x+1)-(90)=0

We multiply parentheses ..

(+8x^2+x+64x+8)-90=0

We get rid of parentheses

8x^2+x+64x+8-90=0

We add all the numbers together, and all the variables

8x^2+65x-82=0

a = 8; b = 65; c = -82;
Δ = b2-4ac
Δ = 652-4·8·(-82)
Δ = 6849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6849}=\sqrt{9*761}=\sqrt{9}*\sqrt{761}=3\sqrt{761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-3\sqrt{761}}{2*8}=\frac{-65-3\sqrt{761}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+3\sqrt{761}}{2*8}=\frac{-65+3\sqrt{761}}{16}
$