((x^2)/20)+8=15

Solution for ((x^2)/20)+8=15 equation:

((x^2)/20)+8=15

We move all terms to the left:

((x^2)/20)+8-(15)=0

We add all the numbers together, and all the variables

(x^2/20)-7=0

We get rid of parentheses

x^2/20-7=0

We multiply all the terms by the denominator


x^2-7*20=0

We add all the numbers together, and all the variables

x^2-140=0

a = 1; b = 0; c = -140;
Δ = b2-4ac
Δ = 02-4·1·(-140)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{35}}{2*1}=\frac{0-4\sqrt{35}}{2}
=-\frac{4\sqrt{35}}{2}
=-2\sqrt{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*1}=\frac{0+4\sqrt{35}}{2}
=\frac{4\sqrt{35}}{2}
=2\sqrt{35}
$