X^2-10x^2+21=0

Solution for X^2-10x^2+21=0 equation:

X^2-10X^2+21=0

We add all the numbers together, and all the variables

-9X^2+21=0

a = -9; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-9)·21
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{21}}{2*-9}=\frac{0-6\sqrt{21}}{-18}
=-\frac{6\sqrt{21}}{-18}
=-\frac{\sqrt{21}}{-3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{21}}{2*-9}=\frac{0+6\sqrt{21}}{-18}
=\frac{6\sqrt{21}}{-18}
=\frac{\sqrt{21}}{-3}
$