414x^2+283x+16=180

Solution for 414x^2+283x+16=180 equation:

414x^2+283x+16=180

We move all terms to the left:

414x^2+283x+16-(180)=0

We add all the numbers together, and all the variables

414x^2+283x-164=0

a = 414; b = 283; c = -164;
Δ = b2-4ac
Δ = 2832-4·414·(-164)
Δ = 351673
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:

$\sqrt{\Delta}=\sqrt{351673}=\sqrt{49*7177}=\sqrt{49}*\sqrt{7177}=7\sqrt{7177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(283)-7\sqrt{7177}}{2*414}=\frac{-283-7\sqrt{7177}}{828}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(283)+7\sqrt{7177}}{2*414}=\frac{-283+7\sqrt{7177}}{828}
$