(5x+38)(8x-19)=180

Solution for (5x+38)(8x-19)=180 equation:

(5x+38)(8x-19)=180

We move all terms to the left:

(5x+38)(8x-19)-(180)=0

We multiply parentheses ..

(+40x^2-95x+304x-722)-180=0

We get rid of parentheses

40x^2-95x+304x-722-180=0

We add all the numbers together, and all the variables

40x^2+209x-902=0

a = 40; b = 209; c = -902;
Δ = b2-4ac
Δ = 2092-4·40·(-902)
Δ = 188001
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:

$\sqrt{\Delta}=\sqrt{188001}=\sqrt{81*2321}=\sqrt{81}*\sqrt{2321}=9\sqrt{2321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(209)-9\sqrt{2321}}{2*40}=\frac{-209-9\sqrt{2321}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(209)+9\sqrt{2321}}{2*40}=\frac{-209+9\sqrt{2321}}{80}
$