(5/2)*x=50

Solution for (5/2)*x=50 equation:

(5/2)*x=50

We move all terms to the left:

(5/2)*x-(50)=0


Domain of the equation: 2)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/2)*x-50=0

We multiply parentheses

5x^2-50=0

a = 5; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·5·(-50)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{10}}{2*5}=\frac{0-10\sqrt{10}}{10}
=-\frac{10\sqrt{10}}{10}
=-\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{10}}{2*5}=\frac{0+10\sqrt{10}}{10}
=\frac{10\sqrt{10}}{10}
=\sqrt{10}
$