0=-73x^2+103x-13

Solution for 0=-73x^2+103x-13 equation:

0=-73x^2+103x-13

We move all terms to the left:

0-(-73x^2+103x-13)=0

We add all the numbers together, and all the variables

-(-73x^2+103x-13)=0

We get rid of parentheses

73x^2-103x+13=0

a = 73; b = -103; c = +13;
Δ = b2-4ac
Δ = -1032-4·73·13
Δ = 6813
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:

$\sqrt{\Delta}=\sqrt{6813}=\sqrt{9*757}=\sqrt{9}*\sqrt{757}=3\sqrt{757}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-103)-3\sqrt{757}}{2*73}=\frac{103-3\sqrt{757}}{146}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-103)+3\sqrt{757}}{2*73}=\frac{103+3\sqrt{757}}{146}
$