2/3x^2+10=90

Solution for 2/3x^2+10=90 equation:

2/3x^2+10=90

We move all terms to the left:

2/3x^2+10-(90)=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x^2-80=0

We multiply all the terms by the denominator


-80*3x^2+2=0

Wy multiply elements

-240x^2+2=0

a = -240; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-240)·2
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*-240}=\frac{0-8\sqrt{30}}{-480}
=-\frac{8\sqrt{30}}{-480}
=-\frac{\sqrt{30}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*-240}=\frac{0+8\sqrt{30}}{-480}
=\frac{8\sqrt{30}}{-480}
=\frac{\sqrt{30}}{-60}
$