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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

4.50(x+3)x

We multiply parentheses

4x^2+12x

Back to the equation:

-(4x^2+12x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2-7.95x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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