.17=x^2/5.25-x

Solution for .17=x^2/5.25-x equation:

.17=x^2/5.25-x

We move all terms to the left:

.17-(x^2/5.25-x)=0


Domain of the equation: 5.25-x)!=0

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

-x)!=-5.25

x!=-5.25/1

x!=-5.25

x∈R


We add all the numbers together, and all the variables

-(x^2/5.25-x)+0.17=0

We get rid of parentheses

-x^2/5.25+x+0.17=0

We multiply all the terms by the denominator


-x^2+x*5.25+(0.17)*5.25=0

We add all the numbers together, and all the variables

-1x^2+x*5.25+0.8925=0

Wy multiply elements

-1x^2+5.25x+0.8925=0

a = -1; b = 5.25; c = +0.8925;
Δ = b2-4ac
Δ = 5.252-4·(-1)·0.8925
Δ = 31.1325
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{-(5.25)-\sqrt{31.1325}}{2*-1}=\frac{-5.25-\sqrt{31.1325}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.25)+\sqrt{31.1325}}{2*-1}=\frac{-5.25+\sqrt{31.1325}}{-2}
$