4x*x-7=x*x

Solution for 4x*x-7=x*x equation:

4x*x-7=x*x

We move all terms to the left:

4x*x-7-(x*x)=0

We add all the numbers together, and all the variables

4x*x-(+x*x)-7=0

Wy multiply elements

4x^2-(+x*x)-7=0

We get rid of parentheses

4x^2-x*x-7=0

Wy multiply elements

4x^2-1x^2-7=0

We add all the numbers together, and all the variables

3x^2-7=0

a = 3; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·3·(-7)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*3}=\frac{0-2\sqrt{21}}{6}
=-\frac{2\sqrt{21}}{6}
=-\frac{\sqrt{21}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*3}=\frac{0+2\sqrt{21}}{6}
=\frac{2\sqrt{21}}{6}
=\frac{\sqrt{21}}{3}
$