2.5=x^2/1.6-x

Solution for 2.5=x^2/1.6-x equation:

2.5=x^2/1.6-x

We move all terms to the left:

2.5-(x^2/1.6-x)=0


Domain of the equation: 1.6-x)!=0

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

-x)!=-1.6

x!=-1.6/1

x!=-1.6

x∈R


We get rid of parentheses

-x^2/1.6+x+2.5=0

We multiply all the terms by the denominator


-x^2+x*1.6+(2.5)*1.6=0

We add all the numbers together, and all the variables

-1x^2+x*1.6+4=0

Wy multiply elements

-1x^2+1.6x+4=0

a = -1; b = 1.6; c = +4;
Δ = b2-4ac
Δ = 1.62-4·(-1)·4
Δ = 18.56
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{-(1.6)-\sqrt{18.56}}{2*-1}=\frac{-1.6-\sqrt{18.56}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.6)+\sqrt{18.56}}{2*-1}=\frac{-1.6+\sqrt{18.56}}{-2}
$