(375+0.5x^2)-(375-0.5x^2)=6935

Solution for (375+0.5x^2)-(375-0.5x^2)=6935 equation:

(375+0.5x^2)-(375-0.5x^2)=6935

We move all terms to the left:

(375+0.5x^2)-(375-0.5x^2)-(6935)=0

We get rid of parentheses

0.5x^2+0.5x^2+375-375-6935=0

We add all the numbers together, and all the variables

x^2-6935=0

a = 1; b = 0; c = -6935;
Δ = b2-4ac
Δ = 02-4·1·(-6935)
Δ = 27740
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:

$\sqrt{\Delta}=\sqrt{27740}=\sqrt{4*6935}=\sqrt{4}*\sqrt{6935}=2\sqrt{6935}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6935}}{2*1}=\frac{0-2\sqrt{6935}}{2}
=-\frac{2\sqrt{6935}}{2}
=-\sqrt{6935}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6935}}{2*1}=\frac{0+2\sqrt{6935}}{2}
=\frac{2\sqrt{6935}}{2}
=\sqrt{6935}
$