2x^2-5x+6.25=10

Solution for 2x^2-5x+6.25=10 equation:

2x^2-5x+6.25=10

We move all terms to the left:

2x^2-5x+6.25-(10)=0

We add all the numbers together, and all the variables

2x^2-5x-3.75=0

a = 2; b = -5; c = -3.75;
Δ = b2-4ac
Δ = -52-4·2·(-3.75)
Δ = 55
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{-(-5)-\sqrt{55}}{2*2}=\frac{5-\sqrt{55}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{55}}{2*2}=\frac{5+\sqrt{55}}{4}
$