196a^2-224a^2+128=0

Solution for 196a^2-224a^2+128=0 equation:

196a^2-224a^2+128=0

We add all the numbers together, and all the variables

-28a^2+128=0

a = -28; b = 0; c = +128;
Δ = b2-4ac
Δ = 02-4·(-28)·128
Δ = 14336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14336}=\sqrt{1024*14}=\sqrt{1024}*\sqrt{14}=32\sqrt{14}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{14}}{2*-28}=\frac{0-32\sqrt{14}}{-56}
=-\frac{32\sqrt{14}}{-56}
=-\frac{4\sqrt{14}}{-7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{14}}{2*-28}=\frac{0+32\sqrt{14}}{-56}
=\frac{32\sqrt{14}}{-56}
=\frac{4\sqrt{14}}{-7}
$