(3x^2)/(.5-2x)=5

Solution for (3x^2)/(.5-2x)=5 equation:

(3x^2)/(.5-2x)=5

We move all terms to the left:

(3x^2)/(.5-2x)-(5)=0


Domain of the equation: (.5-2x)!=0

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

-2x!=-.5

x!=-.5/-2

x!=.5/2

x∈R


We add all the numbers together, and all the variables

3x^2/(-2x+0.5)-5=0

We multiply all the terms by the denominator


3x^2-5*(-2x+0.5)=0

We multiply parentheses

3x^2+10x-2.5=0

a = 3; b = 10; c = -2.5;
Δ = b2-4ac
Δ = 102-4·3·(-2.5)
Δ = 130
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{-(10)-\sqrt{130}}{2*3}=\frac{-10-\sqrt{130}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+\sqrt{130}}{2*3}=\frac{-10+\sqrt{130}}{6}
$