7x^2+4=3x^2+360

Solution for 7x^2+4=3x^2+360 equation:

7x^2+4=3x^2+360

We move all terms to the left:

7x^2+4-(3x^2+360)=0

We get rid of parentheses

7x^2-3x^2-360+4=0

We add all the numbers together, and all the variables

4x^2-356=0

a = 4; b = 0; c = -356;
Δ = b2-4ac
Δ = 02-4·4·(-356)
Δ = 5696
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:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{89}}{2*4}=\frac{0-8\sqrt{89}}{8}
=-\frac{8\sqrt{89}}{8}
=-\sqrt{89}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{89}}{2*4}=\frac{0+8\sqrt{89}}{8}
=\frac{8\sqrt{89}}{8}
=\sqrt{89}
$