x^2-1=0.5x+5

Solution for x^2-1=0.5x+5 equation:

x^2-1=0.5x+5

We move all terms to the left:

x^2-1-(0.5x+5)=0

We get rid of parentheses

x^2-0.5x-5-1=0

We add all the numbers together, and all the variables

x^2-0.5x-6=0

a = 1; b = -0.5; c = -6;
Δ = b2-4ac
Δ = -0.52-4·1·(-6)
Δ = 24.25
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{-(-0.5)-\sqrt{24.25}}{2*1}=\frac{0.5-\sqrt{24.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{24.25}}{2*1}=\frac{0.5+\sqrt{24.25}}{2}
$