X^2=5x^2-140

Solution for X^2=5x^2-140 equation:

X^2=5X^2-140

We move all terms to the left:

X^2-(5X^2-140)=0

We get rid of parentheses

X^2-5X^2+140=0

We add all the numbers together, and all the variables

-4X^2+140=0

a = -4; b = 0; c = +140;
Δ = b2-4ac
Δ = 02-4·(-4)·140
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{35}}{2*-4}=\frac{0-8\sqrt{35}}{-8}
=-\frac{8\sqrt{35}}{-8}
=-\frac{\sqrt{35}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{35}}{2*-4}=\frac{0+8\sqrt{35}}{-8}
=\frac{8\sqrt{35}}{-8}
=\frac{\sqrt{35}}{-1}
$