52=(x/2)(x-5)

Solution for 52=(x/2)(x-5) equation:

52=(x/2)(x-5)

We move all terms to the left:

52-((x/2)(x-5))=0


Domain of the equation: 2)(x-5))!=0

x∈R


We add all the numbers together, and all the variables

-((+x/2)(x-5))+52=0

We multiply parentheses ..

-((+x^2-5x))+52=0


We calculate terms in parentheses: -((+x^2-5x)), so:

(+x^2-5x)

We get rid of parentheses

x^2-5x

Back to the equation:

-(x^2-5x)


We get rid of parentheses

-x^2+5x+52=0

We add all the numbers together, and all the variables

-1x^2+5x+52=0

a = -1; b = 5; c = +52;
Δ = b2-4ac
Δ = 52-4·(-1)·52
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{233}}{2*-1}=\frac{-5-\sqrt{233}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{233}}{2*-1}=\frac{-5+\sqrt{233}}{-2}
$