X(1/4)+x(1.5)=99

Solution for X(1/4)+x(1.5)=99 equation:

X(1/4)+X(1.5)=99

We move all terms to the left:

X(1/4)+X(1.5)-(99)=0

We add all the numbers together, and all the variables

X(+1/4)+X(1.5)-99=0

We multiply parentheses

X^2+1.5X-99=0

a = 1; b = 1.5; c = -99;
Δ = b2-4ac
Δ = 1.52-4·1·(-99)
Δ = 398.25
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{-(1.5)-\sqrt{398.25}}{2*1}=\frac{-1.5-\sqrt{398.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{398.25}}{2*1}=\frac{-1.5+\sqrt{398.25}}{2}
$