6x*x-40=x*x

Solution for 6x*x-40=x*x equation:

6x*x-40=x*x

We move all terms to the left:

6x*x-40-(x*x)=0

We add all the numbers together, and all the variables

6x*x-(+x*x)-40=0

Wy multiply elements

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

We get rid of parentheses

6x^2-x*x-40=0

Wy multiply elements

6x^2-1x^2-40=0

We add all the numbers together, and all the variables

5x^2-40=0

a = 5; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·5·(-40)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*5}=\frac{0-20\sqrt{2}}{10}
=-\frac{20\sqrt{2}}{10}
=-2\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*5}=\frac{0+20\sqrt{2}}{10}
=\frac{20\sqrt{2}}{10}
=2\sqrt{2}
$