10(p+2)8p=61

Solution for 10(p+2)8p=61 equation:

10(p+2)8p=61

We move all terms to the left:

10(p+2)8p-(61)=0

We multiply parentheses

80p^2+160p-61=0

a = 80; b = 160; c = -61;
Δ = b2-4ac
Δ = 1602-4·80·(-61)
Δ = 45120
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:

$\sqrt{\Delta}=\sqrt{45120}=\sqrt{64*705}=\sqrt{64}*\sqrt{705}=8\sqrt{705}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-8\sqrt{705}}{2*80}=\frac{-160-8\sqrt{705}}{160}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+8\sqrt{705}}{2*80}=\frac{-160+8\sqrt{705}}{160}
$