3(5p-5)+8(7p+36)(p=10)

Solution for 3(5p-5)+8(7p+36)(p=10) equation:

3(5p-5)+8(7p+36)(p=10)

We move all terms to the left:

3(5p-5)+8(7p+36)(p-(10))=0

We multiply parentheses

15p+8(7p+36)(p-10)-15=0

We multiply parentheses ..

8(+7p^2-70p+36p-360)+15p-15=0

We multiply parentheses

56p^2-560p+288p+15p-2880-15=0

We add all the numbers together, and all the variables

56p^2-257p-2895=0

a = 56; b = -257; c = -2895;
Δ = b2-4ac
Δ = -2572-4·56·(-2895)
Δ = 714529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-257)-\sqrt{714529}}{2*56}=\frac{257-\sqrt{714529}}{112}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-257)+\sqrt{714529}}{2*56}=\frac{257+\sqrt{714529}}{112}
$