5x^2+2x+1=25

Solution for 5x^2+2x+1=25 equation:

5x^2+2x+1=25

We move all terms to the left:

5x^2+2x+1-(25)=0

We add all the numbers together, and all the variables

5x^2+2x-24=0

a = 5; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·5·(-24)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*5}=\frac{-24}{10}
=-2+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*5}=\frac{20}{10}
=2
$