12x^2+5x^2-7=0

Solution for 12x^2+5x^2-7=0 equation:

12x^2+5x^2-7=0

We add all the numbers together, and all the variables

17x^2-7=0

a = 17; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·17·(-7)
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{119}}{2*17}=\frac{0-2\sqrt{119}}{34}
=-\frac{2\sqrt{119}}{34}
=-\frac{\sqrt{119}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{119}}{2*17}=\frac{0+2\sqrt{119}}{34}
=\frac{2\sqrt{119}}{34}
=\frac{\sqrt{119}}{17}
$