(8x+1)(x+26)=180

Solution for (8x+1)(x+26)=180 equation:

(8x+1)(x+26)=180

We move all terms to the left:

(8x+1)(x+26)-(180)=0

We multiply parentheses ..

(+8x^2+208x+x+26)-180=0

We get rid of parentheses

8x^2+208x+x+26-180=0

We add all the numbers together, and all the variables

8x^2+209x-154=0

a = 8; b = 209; c = -154;
Δ = b2-4ac
Δ = 2092-4·8·(-154)
Δ = 48609
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:

$\sqrt{\Delta}=\sqrt{48609}=\sqrt{9*5401}=\sqrt{9}*\sqrt{5401}=3\sqrt{5401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(209)-3\sqrt{5401}}{2*8}=\frac{-209-3\sqrt{5401}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(209)+3\sqrt{5401}}{2*8}=\frac{-209+3\sqrt{5401}}{16}
$