100=-9p+7(p+12)p=-8p=

Solution for 100=-9p+7(p+12)p=-8p= equation:

100=-9p+7(p+12)p=-8p=

We move all terms to the left:

100-(-9p+7(p+12)p)=0


We calculate terms in parentheses: -(-9p+7(p+12)p), so:

-9p+7(p+12)p

We multiply parentheses

7p^2-9p+84p

We add all the numbers together, and all the variables

7p^2+75p

Back to the equation:

-(7p^2+75p)


We get rid of parentheses

-7p^2-75p+100=0

a = -7; b = -75; c = +100;
Δ = b2-4ac
Δ = -752-4·(-7)·100
Δ = 8425
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:

$\sqrt{\Delta}=\sqrt{8425}=\sqrt{25*337}=\sqrt{25}*\sqrt{337}=5\sqrt{337}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{337}}{2*-7}=\frac{75-5\sqrt{337}}{-14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{337}}{2*-7}=\frac{75+5\sqrt{337}}{-14}
$