5x^2-3x+2.25=27.25

Solution for 5x^2-3x+2.25=27.25 equation:

5x^2-3x+2.25=27.25

We move all terms to the left:

5x^2-3x+2.25-(27.25)=0

We add all the numbers together, and all the variables

5x^2-3x-25=0

a = 5; b = -3; c = -25;
Δ = b2-4ac
Δ = -32-4·5·(-25)
Δ = 509
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{-(-3)-\sqrt{509}}{2*5}=\frac{3-\sqrt{509}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{509}}{2*5}=\frac{3+\sqrt{509}}{10}
$