4x^2-90x+50=1024

Solution for 4x^2-90x+50=1024 equation:

4x^2-90x+50=1024

We move all terms to the left:

4x^2-90x+50-(1024)=0

We add all the numbers together, and all the variables

4x^2-90x-974=0

a = 4; b = -90; c = -974;
Δ = b2-4ac
Δ = -902-4·4·(-974)
Δ = 23684
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:

$\sqrt{\Delta}=\sqrt{23684}=\sqrt{4*5921}=\sqrt{4}*\sqrt{5921}=2\sqrt{5921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{5921}}{2*4}=\frac{90-2\sqrt{5921}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{5921}}{2*4}=\frac{90+2\sqrt{5921}}{8}
$