42x^2=50x^2-20

Solution for 42x^2=50x^2-20 equation:

42x^2=50x^2-20

We move all terms to the left:

42x^2-(50x^2-20)=0

We get rid of parentheses

42x^2-50x^2+20=0

We add all the numbers together, and all the variables

-8x^2+20=0

a = -8; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-8)·20
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-8}=\frac{0-8\sqrt{10}}{-16}
=-\frac{8\sqrt{10}}{-16}
=-\frac{\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-8}=\frac{0+8\sqrt{10}}{-16}
=\frac{8\sqrt{10}}{-16}
=\frac{\sqrt{10}}{-2}
$