X^2-8x/16=50

Solution for X^2-8x/16=50 equation:

X^2-8X/16=50

We move all terms to the left:

X^2-8X/16-(50)=0

We multiply all the terms by the denominator


X^2*16-8X-50*16=0

We add all the numbers together, and all the variables

X^2*16-8X-800=0

Wy multiply elements

16X^2-8X-800=0

a = 16; b = -8; c = -800;
Δ = b2-4ac
Δ = -82-4·16·(-800)
Δ = 51264
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:

$\sqrt{\Delta}=\sqrt{51264}=\sqrt{576*89}=\sqrt{576}*\sqrt{89}=24\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24\sqrt{89}}{2*16}=\frac{8-24\sqrt{89}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24\sqrt{89}}{2*16}=\frac{8+24\sqrt{89}}{32}
$