25x^2-14x+2=50

Solution for 25x^2-14x+2=50 equation:

25x^2-14x+2=50

We move all terms to the left:

25x^2-14x+2-(50)=0

We add all the numbers together, and all the variables

25x^2-14x-48=0

a = 25; b = -14; c = -48;
Δ = b2-4ac
Δ = -142-4·25·(-48)
Δ = 4996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4996}=\sqrt{4*1249}=\sqrt{4}*\sqrt{1249}=2\sqrt{1249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{1249}}{2*25}=\frac{14-2\sqrt{1249}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{1249}}{2*25}=\frac{14+2\sqrt{1249}}{50}
$