1.5(x)=-16x^2+272x

Solution for 1.5(x)=-16x^2+272x equation:

1.5(x)=-16x^2+272x

We move all terms to the left:

1.5(x)-(-16x^2+272x)=0

We get rid of parentheses

16x^2-272x+1.5x=0

We add all the numbers together, and all the variables

16x^2-270.5x=0

a = 16; b = -270.5; c = 0;
Δ = b2-4ac
Δ = -270.52-4·16·0
Δ = 73170.25
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{-(-270.5)-\sqrt{73170.25}}{2*16}=\frac{270.5-\sqrt{73170.25}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270.5)+\sqrt{73170.25}}{2*16}=\frac{270.5+\sqrt{73170.25}}{32}
$