43245x^2+(18500x^2)+(76123x^2)=15

Solution for 43245x^2+(18500x^2)+(76123x^2)=15 equation:

43245x^2+(18500x^2)+(76123x^2)=15

We move all terms to the left:

43245x^2+(18500x^2)+(76123x^2)-(15)=0

We add all the numbers together, and all the variables

137868x^2-15=0

a = 137868; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·137868·(-15)
Δ = 8272080
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:

$\sqrt{\Delta}=\sqrt{8272080}=\sqrt{144*57445}=\sqrt{144}*\sqrt{57445}=12\sqrt{57445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{57445}}{2*137868}=\frac{0-12\sqrt{57445}}{275736}
=-\frac{12\sqrt{57445}}{275736}
=-\frac{\sqrt{57445}}{22978}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{57445}}{2*137868}=\frac{0+12\sqrt{57445}}{275736}
=\frac{12\sqrt{57445}}{275736}
=\frac{\sqrt{57445}}{22978}
$