40^2=6x^2+3x^2

Solution for 40^2=6x^2+3x^2 equation:

40^2=6x^2+3x^2

We move all terms to the left:

40^2-(6x^2+3x^2)=0

We add all the numbers together, and all the variables

-(6x^2+3x^2)+1600=0

We get rid of parentheses

-6x^2-3x^2+1600=0

We add all the numbers together, and all the variables

-9x^2+1600=0

a = -9; b = 0; c = +1600;
Δ = b2-4ac
Δ = 02-4·(-9)·1600
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240}{2*-9}=\frac{-240}{-18}
=13+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240}{2*-9}=\frac{240}{-18}
=-13+1/3
$