0.20=x2/35-x

Solution for 0.20=x2/35-x equation:

0.20=x2/35-x

We move all terms to the left:

0.20-(x2/35-x)=0


Domain of the equation: 35-x)!=0

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

-x)!=-35

x!=-35/1

x!=-35

x∈R


We add all the numbers together, and all the variables

-(-1x+x2/35)+0.20=0

We add all the numbers together, and all the variables

-(-1x+x2/35)+0.2=0

We get rid of parentheses

1x-x2/35+0.2=0

We multiply all the terms by the denominator


1x*35-x2+(0.2)*35=0

We add all the numbers together, and all the variables

-1x^2+1x*35+7=0

Wy multiply elements

-1x^2+35x+7=0

a = -1; b = 35; c = +7;
Δ = b2-4ac
Δ = 352-4·(-1)·7
Δ = 1253
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{-(35)-\sqrt{1253}}{2*-1}=\frac{-35-\sqrt{1253}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1253}}{2*-1}=\frac{-35+\sqrt{1253}}{-2}
$