4x^2+180x+1000=0

Solution for 4x^2+180x+1000=0 equation:

4x^2+180x+1000=0

a = 4; b = 180; c = +1000;
Δ = b2-4ac
Δ = 1802-4·4·1000
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-20\sqrt{41}}{2*4}=\frac{-180-20\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+20\sqrt{41}}{2*4}=\frac{-180+20\sqrt{41}}{8}
$