49x^2=14x+1

Solution for 49x^2=14x+1 equation:

49x^2=14x+1

We move all terms to the left:

49x^2-(14x+1)=0

We get rid of parentheses

49x^2-14x-1=0

a = 49; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·49·(-1)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{2}}{2*49}=\frac{14-14\sqrt{2}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{2}}{2*49}=\frac{14+14\sqrt{2}}{98}
$