6=90-p2/10

Solution for 6=90-p2/10 equation:

6=90-p2/10

We move all terms to the left:

6-(90-p2/10)=0

We add all the numbers together, and all the variables

-(-p2/10+90)+6=0

We get rid of parentheses

p2/10-90+6=0

We multiply all the terms by the denominator


p2-90*10+6*10=0

We add all the numbers together, and all the variables

p^2-840=0

a = 1; b = 0; c = -840;
Δ = b2-4ac
Δ = 02-4·1·(-840)
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*1}=\frac{0-4\sqrt{210}}{2}
=-\frac{4\sqrt{210}}{2}
=-2\sqrt{210}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*1}=\frac{0+4\sqrt{210}}{2}
=\frac{4\sqrt{210}}{2}
=2\sqrt{210}
$