x^2=2.5x+6.5

Solution for x^2=2.5x+6.5 equation:

x^2=2.5x+6.5

We move all terms to the left:

x^2-(2.5x+6.5)=0

We get rid of parentheses

x^2-2.5x-6.5=0

a = 1; b = -2.5; c = -6.5;
Δ = b2-4ac
Δ = -2.52-4·1·(-6.5)
Δ = 32.25
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{32.25}}{2*1}=\frac{2.5-\sqrt{32.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{32.25}}{2*1}=\frac{2.5+\sqrt{32.25}}{2}
$