2=1.5p^2/7

Solution for 2=1.5p^2/7 equation:

2=1.5p^2/7

We move all terms to the left:

2-(1.5p^2/7)=0

We get rid of parentheses

-1.5p^2/7+2=0

We multiply all the terms by the denominator


-1.5p^2+2*7=0

We add all the numbers together, and all the variables

-1.5p^2+14=0

a = -1.5; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-1.5)·14
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-1.5}=\frac{0-2\sqrt{21}}{-3}
=-\frac{2\sqrt{21}}{-3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-1.5}=\frac{0+2\sqrt{21}}{-3}
=\frac{2\sqrt{21}}{-3}
$