5p^2+10p=46

Solution for 5p^2+10p=46 equation:

5p^2+10p=46

We move all terms to the left:

5p^2+10p-(46)=0

a = 5; b = 10; c = -46;
Δ = b2-4ac
Δ = 102-4·5·(-46)
Δ = 1020
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:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{255}}{2*5}=\frac{-10-2\sqrt{255}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{255}}{2*5}=\frac{-10+2\sqrt{255}}{10}
$