15x^2-196x+196=0

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Solution for 15x^2-196x+196=0 equation:



15x^2-196x+196=0
a = 15; b = -196; c = +196;
Δ = b2-4ac
Δ = -1962-4·15·196
Δ = 26656
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:
$\sqrt{\Delta}=\sqrt{26656}=\sqrt{784*34}=\sqrt{784}*\sqrt{34}=28\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-28\sqrt{34}}{2*15}=\frac{196-28\sqrt{34}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+28\sqrt{34}}{2*15}=\frac{196+28\sqrt{34}}{30} $

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