186=(4x^2+8x)/2x

Solution for 186=(4x^2+8x)/2x equation:

186=(4x^2+8x)/2x

We move all terms to the left:

186-((4x^2+8x)/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-((4x^2+8x)+186*2x)=0


We calculate terms in parentheses: -((4x^2+8x)+186*2x), so:

(4x^2+8x)+186*2x

Wy multiply elements

(4x^2+8x)+372x

We get rid of parentheses

4x^2+8x+372x

We add all the numbers together, and all the variables

4x^2+380x

Back to the equation:

-(4x^2+380x)


We get rid of parentheses

-4x^2-380x=0

a = -4; b = -380; c = 0;
Δ = b2-4ac
Δ = -3802-4·(-4)·0
Δ = 144400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144400}=380$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-380}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+380}{2*-4}=\frac{760}{-8}
=-95
$