5x^2-25x+4=-24

Solution for 5x^2-25x+4=-24 equation:

5x^2-25x+4=-24

We move all terms to the left:

5x^2-25x+4-(-24)=0

We add all the numbers together, and all the variables

5x^2-25x+28=0

a = 5; b = -25; c = +28;
Δ = b2-4ac
Δ = -252-4·5·28
Δ = 65
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{-(-25)-\sqrt{65}}{2*5}=\frac{25-\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{65}}{2*5}=\frac{25+\sqrt{65}}{10}
$