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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

4.05p-(4.50(p+3)4.05p+14.40)+14.4=0


We calculate terms in parentheses: -(4.50(p+3)4.05p+14.40), so:

4.50(p+3)4.05p+14.40

We add all the numbers together, and all the variables

4.50(p+3)4.05p+14.4

We multiply parentheses

18p^2+54p+14.4

Back to the equation:

-(18p^2+54p+14.4)


We get rid of parentheses

-18p^2+4.05p-54p-14.4+14.4=0

We add all the numbers together, and all the variables

-18p^2-49.95p=0

a = -18; b = -49.95; c = 0;
Δ = b2-4ac
Δ = -49.952-4·(-18)·0
Δ = 2495.0025
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{-(-49.95)-\sqrt{2495.0025}}{2*-18}=\frac{49.95-\sqrt{2495.0025}}{-36}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49.95)+\sqrt{2495.0025}}{2*-18}=\frac{49.95+\sqrt{2495.0025}}{-36}
$