7x2-160=5x2+160

Solution for 7x2-160=5x2+160 equation:

7x^2-160=5x^2+160

We move all terms to the left:

7x^2-160-(5x^2+160)=0

We get rid of parentheses

7x^2-5x^2-160-160=0

We add all the numbers together, and all the variables

2x^2-320=0

a = 2; b = 0; c = -320;
Δ = b2-4ac
Δ = 02-4·2·(-320)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{10}}{2*2}=\frac{0-16\sqrt{10}}{4}
=-\frac{16\sqrt{10}}{4}
=-4\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{10}}{2*2}=\frac{0+16\sqrt{10}}{4}
=\frac{16\sqrt{10}}{4}
=4\sqrt{10}
$