7(3p-1)(-p+5)=-52

Solution for 7(3p-1)(-p+5)=-52 equation:

7(3p-1)(-p+5)=-52

We move all terms to the left:

7(3p-1)(-p+5)-(-52)=0

We add all the numbers together, and all the variables

7(3p-1)(-1p+5)-(-52)=0

We add all the numbers together, and all the variables

7(3p-1)(-1p+5)+52=0

We multiply parentheses ..

7(-3p^2+15p+p-5)+52=0

We multiply parentheses

-21p^2+105p+7p-35+52=0

We add all the numbers together, and all the variables

-21p^2+112p+17=0

a = -21; b = 112; c = +17;
Δ = b2-4ac
Δ = 1122-4·(-21)·17
Δ = 13972
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:

$\sqrt{\Delta}=\sqrt{13972}=\sqrt{4*3493}=\sqrt{4}*\sqrt{3493}=2\sqrt{3493}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-2\sqrt{3493}}{2*-21}=\frac{-112-2\sqrt{3493}}{-42}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+2\sqrt{3493}}{2*-21}=\frac{-112+2\sqrt{3493}}{-42}
$