10x-x^2-18.75=0

Solution for 10x-x^2-18.75=0 equation:

10x-x^2-18.75=0

We add all the numbers together, and all the variables

-1x^2+10x-18.75=0

a = -1; b = 10; c = -18.75;
Δ = b2-4ac
Δ = 102-4·(-1)·(-18.75)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-5}{2*-1}=\frac{-15}{-2}
=7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+5}{2*-1}=\frac{-5}{-2}
=2+1/2
$