5p^2+10p-53=6

Solution for 5p^2+10p-53=6 equation:

5p^2+10p-53=6

We move all terms to the left:

5p^2+10p-53-(6)=0

We add all the numbers together, and all the variables

5p^2+10p-59=0

a = 5; b = 10; c = -59;
Δ = b2-4ac
Δ = 102-4·5·(-59)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-16\sqrt{5}}{2*5}=\frac{-10-16\sqrt{5}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+16\sqrt{5}}{2*5}=\frac{-10+16\sqrt{5}}{10}
$