7^2x^2-5x=1/49

Solution for 7^2x^2-5x=1/49 equation:

7^2x^2-5x=1/49

We move all terms to the left:

7^2x^2-5x-(1/49)=0

We add all the numbers together, and all the variables

7^2x^2-5x-(+1/49)=0

We add all the numbers together, and all the variables

-5x+7^2x^2-(+1/49)=0

We get rid of parentheses

-5x+7^2x^2-1/49=0

We multiply all the terms by the denominator


-5x*49+7^2x^2*49-1=0

Wy multiply elements

343x^2-245x-1=0

a = 343; b = -245; c = -1;
Δ = b2-4ac
Δ = -2452-4·343·(-1)
Δ = 61397
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:

$\sqrt{\Delta}=\sqrt{61397}=\sqrt{49*1253}=\sqrt{49}*\sqrt{1253}=7\sqrt{1253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-245)-7\sqrt{1253}}{2*343}=\frac{245-7\sqrt{1253}}{686}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-245)+7\sqrt{1253}}{2*343}=\frac{245+7\sqrt{1253}}{686}
$