14x^2-49x^2+21=0

Solution for 14x^2-49x^2+21=0 equation:

14x^2-49x^2+21=0

We add all the numbers together, and all the variables

-35x^2+21=0

a = -35; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-35)·21
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{15}}{2*-35}=\frac{0-14\sqrt{15}}{-70}
=-\frac{14\sqrt{15}}{-70}
=-\frac{\sqrt{15}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{15}}{2*-35}=\frac{0+14\sqrt{15}}{-70}
=\frac{14\sqrt{15}}{-70}
=\frac{\sqrt{15}}{-5}
$