5=(x^2)/20+1.5

Solution for 5=(x^2)/20+1.5 equation:

5=(x^2)/20+1.5

We move all terms to the left:

5-((x^2)/20+1.5)=0

We get rid of parentheses

-x^2/20-1.5+5=0

We multiply all the terms by the denominator


-x^2-(1.5)*20+5*20=0

We add all the numbers together, and all the variables

-1x^2+70=0

a = -1; b = 0; c = +70;
Δ = b2-4ac
Δ = 02-4·(-1)·70
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*-1}=\frac{0-2\sqrt{70}}{-2}
=-\frac{2\sqrt{70}}{-2}
=-\frac{\sqrt{70}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*-1}=\frac{0+2\sqrt{70}}{-2}
=\frac{2\sqrt{70}}{-2}
=\frac{\sqrt{70}}{-1}
$