28x^2+1024x-2037=10283

Solution for 28x^2+1024x-2037=10283 equation:

28x^2+1024x-2037=10283

We move all terms to the left:

28x^2+1024x-2037-(10283)=0

We add all the numbers together, and all the variables

28x^2+1024x-12320=0

a = 28; b = 1024; c = -12320;
Δ = b2-4ac
Δ = 10242-4·28·(-12320)
Δ = 2428416
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:

$\sqrt{\Delta}=\sqrt{2428416}=\sqrt{2304*1054}=\sqrt{2304}*\sqrt{1054}=48\sqrt{1054}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1024)-48\sqrt{1054}}{2*28}=\frac{-1024-48\sqrt{1054}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1024)+48\sqrt{1054}}{2*28}=\frac{-1024+48\sqrt{1054}}{56}
$