7x^2+12=51-4x^2

Solution for 7x^2+12=51-4x^2 equation:

7x^2+12=51-4x^2

We move all terms to the left:

7x^2+12-(51-4x^2)=0

We get rid of parentheses

7x^2+4x^2-51+12=0

We add all the numbers together, and all the variables

11x^2-39=0

a = 11; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·11·(-39)
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{429}}{2*11}=\frac{0-2\sqrt{429}}{22}
=-\frac{2\sqrt{429}}{22}
=-\frac{\sqrt{429}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{429}}{2*11}=\frac{0+2\sqrt{429}}{22}
=\frac{2\sqrt{429}}{22}
=\frac{\sqrt{429}}{11}
$