2x-x^2/100=51

Solution for 2x-x^2/100=51 equation:

2x-x^2/100=51

We move all terms to the left:

2x-x^2/100-(51)=0

We multiply all the terms by the denominator


-x^2+2x*100-51*100=0

We add all the numbers together, and all the variables

-1x^2+2x*100-5100=0

Wy multiply elements

-1x^2+200x-5100=0

a = -1; b = 200; c = -5100;
Δ = b2-4ac
Δ = 2002-4·(-1)·(-5100)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-140}{2*-1}=\frac{-340}{-2}
=+170
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+140}{2*-1}=\frac{-60}{-2}
=+30
$