5x^2=1.5x

Solution for 5x^2=1.5x equation:

5x^2=1.5x

We move all terms to the left:

5x^2-(1.5x)=0

We add all the numbers together, and all the variables

5x^2-(+1.5x)=0

We get rid of parentheses

5x^2-1.5x=0

a = 5; b = -1.5; c = 0;
Δ = b2-4ac
Δ = -1.52-4·5·0
Δ = 2.25
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{-(-1.5)-\sqrt{2.25}}{2*5}=\frac{1.5-\sqrt{2.25}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{2.25}}{2*5}=\frac{1.5+\sqrt{2.25}}{10}
$