234x^2+(546x^2)-(352x^2)+(1234x^2)-(8x^2)+(2354x^2)+(5555x^2)=17

Solution for 234x^2+(546x^2)-(352x^2)+(1234x^2)-(8x^2)+(2354x^2)+(5555x^2)=17 equation:

234x^2+(546x^2)-(352x^2)+(1234x^2)-(8x^2)+(2354x^2)+(5555x^2)=17

We move all terms to the left:

234x^2+(546x^2)-(352x^2)+(1234x^2)-(8x^2)+(2354x^2)+(5555x^2)-(17)=0

We add all the numbers together, and all the variables

9563x^2-17=0

a = 9563; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·9563·(-17)
Δ = 650284
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:

$\sqrt{\Delta}=\sqrt{650284}=\sqrt{4*162571}=\sqrt{4}*\sqrt{162571}=2\sqrt{162571}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{162571}}{2*9563}=\frac{0-2\sqrt{162571}}{19126}
=-\frac{2\sqrt{162571}}{19126}
=-\frac{\sqrt{162571}}{9563}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{162571}}{2*9563}=\frac{0+2\sqrt{162571}}{19126}
=\frac{2\sqrt{162571}}{19126}
=\frac{\sqrt{162571}}{9563}
$