4.05p+14.40=4.50(p+3)p=

Solution for 4.05p+14.40=4.50(p+3)p= equation:

4.05p+14.40=4.50(p+3)p=

We move all terms to the left:

4.05p+14.40-(4.50(p+3)p)=0

We add all the numbers together, and all the variables

4.05p-(4.50(p+3)p)+14.4=0


We calculate terms in parentheses: -(4.50(p+3)p), so:

4.50(p+3)p

We multiply parentheses

4p^2+12p

Back to the equation:

-(4p^2+12p)


We get rid of parentheses

-4p^2+4.05p-12p+14.4=0

We add all the numbers together, and all the variables

-4p^2-7.95p+14.4=0

a = -4; b = -7.95; c = +14.4;
Δ = b2-4ac
Δ = -7.952-4·(-4)·14.4
Δ = 293.6025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7.95)-\sqrt{293.6025}}{2*-4}=\frac{7.95-\sqrt{293.6025}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.95)+\sqrt{293.6025}}{2*-4}=\frac{7.95+\sqrt{293.6025}}{-8}
$