17-x^2/4=43-x^2

Solution for 17-x^2/4=43-x^2 equation:

17-x^2/4=43-x^2

We move all terms to the left:

17-x^2/4-(43-x^2)=0

We get rid of parentheses

-x^2/4+x^2-43+17=0

We multiply all the terms by the denominator


-x^2+x^2*4-43*4+17*4=0

We add all the numbers together, and all the variables

-1x^2+x^2*4-104=0

Wy multiply elements

-1x^2+4x^2-104=0

We add all the numbers together, and all the variables

3x^2-104=0

a = 3; b = 0; c = -104;
Δ = b2-4ac
Δ = 02-4·3·(-104)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{78}}{2*3}=\frac{0-4\sqrt{78}}{6}
=-\frac{4\sqrt{78}}{6}
=-\frac{2\sqrt{78}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{78}}{2*3}=\frac{0+4\sqrt{78}}{6}
=\frac{4\sqrt{78}}{6}
=\frac{2\sqrt{78}}{3}
$