x*x=100*x/2

Solution for x*x=100*x/2 equation:

x*x=100x/2

We move all terms to the left:

x*x-(100x/2)=0

We add all the numbers together, and all the variables

x*x-(+100x/2)=0

Wy multiply elements

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

We get rid of parentheses

x^2-100x/2=0

We multiply all the terms by the denominator


x^2*2-100x=0

Wy multiply elements

2x^2-100x=0

a = 2; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·2·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*2}=\frac{200}{4}
=50
$