16x^2-196x+369=9

Solution for 16x^2-196x+369=9 equation:

16x^2-196x+369=9

We move all terms to the left:

16x^2-196x+369-(9)=0

We add all the numbers together, and all the variables

16x^2-196x+360=0

a = 16; b = -196; c = +360;
Δ = b2-4ac
Δ = -1962-4·16·360
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-124}{2*16}=\frac{72}{32}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+124}{2*16}=\frac{320}{32}
=10
$