X2-2.5x-51=0

Solution for X2-2.5x-51=0 equation:

X2-2.5X-51=0

We add all the numbers together, and all the variables

X^2-2.5X-51=0

a = 1; b = -2.5; c = -51;
Δ = b2-4ac
Δ = -2.52-4·1·(-51)
Δ = 210.25
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{-(-2.5)-\sqrt{210.25}}{2*1}=\frac{2.5-\sqrt{210.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{210.25}}{2*1}=\frac{2.5+\sqrt{210.25}}{2}
$