4x^2-280x+4800=1000

Solution for 4x^2-280x+4800=1000 equation:

4x^2-280x+4800=1000

We move all terms to the left:

4x^2-280x+4800-(1000)=0

We add all the numbers together, and all the variables

4x^2-280x+3800=0

a = 4; b = -280; c = +3800;
Δ = b2-4ac
Δ = -2802-4·4·3800
Δ = 17600
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:

$\sqrt{\Delta}=\sqrt{17600}=\sqrt{1600*11}=\sqrt{1600}*\sqrt{11}=40\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-40\sqrt{11}}{2*4}=\frac{280-40\sqrt{11}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+40\sqrt{11}}{2*4}=\frac{280+40\sqrt{11}}{8}
$