5x+20x2+9x-92=180

Solution for 5x+20x2+9x-92=180 equation:

5x+20x^2+9x-92=180

We move all terms to the left:

5x+20x^2+9x-92-(180)=0

We add all the numbers together, and all the variables

20x^2+14x-272=0

a = 20; b = 14; c = -272;
Δ = b2-4ac
Δ = 142-4·20·(-272)
Δ = 21956
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:

$\sqrt{\Delta}=\sqrt{21956}=\sqrt{4*5489}=\sqrt{4}*\sqrt{5489}=2\sqrt{5489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{5489}}{2*20}=\frac{-14-2\sqrt{5489}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{5489}}{2*20}=\frac{-14+2\sqrt{5489}}{40}
$