0.25x(102-x)=23.50

Solution for 0.25x(102-x)=23.50 equation:

0.25x(102-x)=23.50

We move all terms to the left:

0.25x(102-x)-(23.50)=0

We add all the numbers together, and all the variables

0.25x(-1x+102)-(23.5)=0

We add all the numbers together, and all the variables

0.25x(-1x+102)-23.5=0

We multiply parentheses

0x^2+0x-23.5=0

We add all the numbers together, and all the variables

x^2+x-23.5=0

a = 1; b = 1; c = -23.5;
Δ = b2-4ac
Δ = 12-4·1·(-23.5)
Δ = 95
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{-(1)-\sqrt{95}}{2*1}=\frac{-1-\sqrt{95}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{95}}{2*1}=\frac{-1+\sqrt{95}}{2}
$