0=9x^2-100x+196

Solution for 0=9x^2-100x+196 equation:

0=9x^2-100x+196

We move all terms to the left:

0-(9x^2-100x+196)=0

We add all the numbers together, and all the variables

-(9x^2-100x+196)=0

We get rid of parentheses

-9x^2+100x-196=0

a = -9; b = 100; c = -196;
Δ = b2-4ac
Δ = 1002-4·(-9)·(-196)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-8\sqrt{46}}{2*-9}=\frac{-100-8\sqrt{46}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+8\sqrt{46}}{2*-9}=\frac{-100+8\sqrt{46}}{-18}
$