Hx2/3=10

Solution for Hx2/3=10 equation:

H2/3=10

We move all terms to the left:

H2/3-(10)=0

We multiply all the terms by the denominator


H2-10*3=0

We add all the numbers together, and all the variables

H^2-30=0

a = 1; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·1·(-30)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*1}=\frac{0-2\sqrt{30}}{2}
=-\frac{2\sqrt{30}}{2}
=-\sqrt{30}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*1}=\frac{0+2\sqrt{30}}{2}
=\frac{2\sqrt{30}}{2}
=\sqrt{30}
$