x(x+1/2)=24.75

Solution for x(x+1/2)=24.75 equation:

x(x+1/2)=24.75

We move all terms to the left:

x(x+1/2)-(24.75)=0

We add all the numbers together, and all the variables

x(+x+1/2)-(24.75)=0

We add all the numbers together, and all the variables

x(+x+1/2)-24.75=0

We multiply parentheses

x^2+x^2-24.75=0

We add all the numbers together, and all the variables

2x^2-24.75=0

a = 2; b = 0; c = -24.75;
Δ = b2-4ac
Δ = 02-4·2·(-24.75)
Δ = 198
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:

$\sqrt{\Delta}=\sqrt{198}=\sqrt{9*22}=\sqrt{9}*\sqrt{22}=3\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{22}}{2*2}=\frac{0-3\sqrt{22}}{4}
=-\frac{3\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{22}}{2*2}=\frac{0+3\sqrt{22}}{4}
=\frac{3\sqrt{22}}{4}
$