-6p+7=(6p-9)(40-16p)

Solution for -6p+7=(6p-9)(40-16p) equation:

-6p+7=(6p-9)(40-16p)

We move all terms to the left:

-6p+7-((6p-9)(40-16p))=0

We add all the numbers together, and all the variables

-6p-((6p-9)(-16p+40))+7=0

We multiply parentheses ..

-((-96p^2+240p+144p-360))-6p+7=0


We calculate terms in parentheses: -((-96p^2+240p+144p-360)), so:

(-96p^2+240p+144p-360)

We get rid of parentheses

-96p^2+240p+144p-360

We add all the numbers together, and all the variables

-96p^2+384p-360

Back to the equation:

-(-96p^2+384p-360)


We get rid of parentheses

96p^2-384p-6p+360+7=0

We add all the numbers together, and all the variables

96p^2-390p+367=0

a = 96; b = -390; c = +367;
Δ = b2-4ac
Δ = -3902-4·96·367
Δ = 11172
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:

$\sqrt{\Delta}=\sqrt{11172}=\sqrt{196*57}=\sqrt{196}*\sqrt{57}=14\sqrt{57}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-390)-14\sqrt{57}}{2*96}=\frac{390-14\sqrt{57}}{192}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-390)+14\sqrt{57}}{2*96}=\frac{390+14\sqrt{57}}{192}
$