53.3=2x^2/0.4-x

Solution for 53.3=2x^2/0.4-x equation:

53.3=2x^2/0.4-x

We move all terms to the left:

53.3-(2x^2/0.4-x)=0


Domain of the equation: 0.4-x)!=0

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

-x)!=-0.4

x!=-0.4/1

x!=-0.4

x∈R


We get rid of parentheses

-2x^2/0.4+x+53.3=0

We multiply all the terms by the denominator


-2x^2+x*0.4+(53.3)*0.4=0

We add all the numbers together, and all the variables

-2x^2+x*0.4+21.32=0

Wy multiply elements

-2x^2+0.4x+21.32=0

a = -2; b = 0.4; c = +21.32;
Δ = b2-4ac
Δ = 0.42-4·(-2)·21.32
Δ = 170.72
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{-(0.4)-\sqrt{170.72}}{2*-2}=\frac{-0.4-\sqrt{170.72}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.4)+\sqrt{170.72}}{2*-2}=\frac{-0.4+\sqrt{170.72}}{-4}
$