280=3/2*x

Solution for 280=3/2*x equation:

280=3/2*x

We move all terms to the left:

280-(3/2*x)=0


Domain of the equation: 2*x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+3/2*x)+280=0

We get rid of parentheses

-3/2*x+280=0

We multiply all the terms by the denominator


280*2*x-3=0

Wy multiply elements

560x*x-3=0

Wy multiply elements

560x^2-3=0

a = 560; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·560·(-3)
Δ = 6720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{105}}{2*560}=\frac{0-8\sqrt{105}}{1120}
=-\frac{8\sqrt{105}}{1120}
=-\frac{\sqrt{105}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{105}}{2*560}=\frac{0+8\sqrt{105}}{1120}
=\frac{8\sqrt{105}}{1120}
=\frac{\sqrt{105}}{140}
$