-7p(p-6)=18-4p

Solution for -7p(p-6)=18-4p equation:

-7p(p-6)=18-4p

We move all terms to the left:

-7p(p-6)-(18-4p)=0

We add all the numbers together, and all the variables

-7p(p-6)-(-4p+18)=0

We multiply parentheses

-7p^2+42p-(-4p+18)=0

We get rid of parentheses

-7p^2+42p+4p-18=0

We add all the numbers together, and all the variables

-7p^2+46p-18=0

a = -7; b = 46; c = -18;
Δ = b2-4ac
Δ = 462-4·(-7)·(-18)
Δ = 1612
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:

$\sqrt{\Delta}=\sqrt{1612}=\sqrt{4*403}=\sqrt{4}*\sqrt{403}=2\sqrt{403}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{403}}{2*-7}=\frac{-46-2\sqrt{403}}{-14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{403}}{2*-7}=\frac{-46+2\sqrt{403}}{-14}
$