1=13x^2-7x

Solution for 1=13x^2-7x equation:

1=13x^2-7x

We move all terms to the left:

1-(13x^2-7x)=0

We get rid of parentheses

-13x^2+7x+1=0

a = -13; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-13)·1
Δ = 101
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{-(7)-\sqrt{101}}{2*-13}=\frac{-7-\sqrt{101}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{101}}{2*-13}=\frac{-7+\sqrt{101}}{-26}
$