5x^2-5x+8=25

Solution for 5x^2-5x+8=25 equation:

5x^2-5x+8=25

We move all terms to the left:

5x^2-5x+8-(25)=0

We add all the numbers together, and all the variables

5x^2-5x-17=0

a = 5; b = -5; c = -17;
Δ = b2-4ac
Δ = -52-4·5·(-17)
Δ = 365
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{365}}{2*5}=\frac{5-\sqrt{365}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{365}}{2*5}=\frac{5+\sqrt{365}}{10}
$