(2x+9)(4x-41)=180

Solution for (2x+9)(4x-41)=180 equation:

(2x+9)(4x-41)=180

We move all terms to the left:

(2x+9)(4x-41)-(180)=0

We multiply parentheses ..

(+8x^2-82x+36x-369)-180=0

We get rid of parentheses

8x^2-82x+36x-369-180=0

We add all the numbers together, and all the variables

8x^2-46x-549=0

a = 8; b = -46; c = -549;
Δ = b2-4ac
Δ = -462-4·8·(-549)
Δ = 19684
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:

$\sqrt{\Delta}=\sqrt{19684}=\sqrt{4*4921}=\sqrt{4}*\sqrt{4921}=2\sqrt{4921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{4921}}{2*8}=\frac{46-2\sqrt{4921}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{4921}}{2*8}=\frac{46+2\sqrt{4921}}{16}
$