0.75*(x)^2-(x)-2.5=0

Solution for 0.75*(x)^2-(x)-2.5=0 equation:

0.75(x)^2-(x)-2.5=0

We add all the numbers together, and all the variables

0.75x^2-1x-2.5=0

a = 0.75; b = -1; c = -2.5;
Δ = b2-4ac
Δ = -12-4·0.75·(-2.5)
Δ = 8.5
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{8.5}}{2*0.75}=\frac{1-\sqrt{8.5}}{1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{8.5}}{2*0.75}=\frac{1+\sqrt{8.5}}{1.5}
$