4p-7=-7(2p+3)+8(-6+p2)

Solution for 4p-7=-7(2p+3)+8(-6+p2) equation:

4p-7=-7(2p+3)+8(-6+p2)

We move all terms to the left:

4p-7-(-7(2p+3)+8(-6+p2))=0

We add all the numbers together, and all the variables

-(-7(2p+3)+8(+p^2-6))+4p-7=0


We calculate terms in parentheses: -(-7(2p+3)+8(+p^2-6)), so:

-7(2p+3)+8(+p^2-6)

determiningTheFunctionDomain
8(+p^2-6)-7(2p+3)

We multiply parentheses

8p^2-14p-48-21

We add all the numbers together, and all the variables

8p^2-14p-69

Back to the equation:

-(8p^2-14p-69)


We add all the numbers together, and all the variables

4p-(8p^2-14p-69)-7=0

We get rid of parentheses

-8p^2+4p+14p+69-7=0

We add all the numbers together, and all the variables

-8p^2+18p+62=0

a = -8; b = 18; c = +62;
Δ = b2-4ac
Δ = 182-4·(-8)·62
Δ = 2308
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:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{577}}{2*-8}=\frac{-18-2\sqrt{577}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{577}}{2*-8}=\frac{-18+2\sqrt{577}}{-16}
$