1.5=(2x)^2/5-x

Solution for 1.5=(2x)^2/5-x equation:

1.5=(2x)^2/5-x

We move all terms to the left:

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


Domain of the equation: 5-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-5

x!=-5/1

x!=-5

x∈R


We get rid of parentheses

-2x^2/5+x+1.5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x^2+x*5+7.5=0

Wy multiply elements

-2x^2+5x+7.5=0

a = -2; b = 5; c = +7.5;
Δ = b2-4ac
Δ = 52-4·(-2)·7.5
Δ = 85
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{-(5)-\sqrt{85}}{2*-2}=\frac{-5-\sqrt{85}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*-2}=\frac{-5+\sqrt{85}}{-4}
$