78/x=2x+3

Solution for 78/x=2x+3 equation:

78/x=2x+3

We move all terms to the left:

78/x-(2x+3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

78/x-2x-3=0

We multiply all the terms by the denominator


-2x*x-3*x+78=0

We add all the numbers together, and all the variables

-3x-2x*x+78=0

Wy multiply elements

-2x^2-3x+78=0

a = -2; b = -3; c = +78;
Δ = b2-4ac
Δ = -32-4·(-2)·78
Δ = 633
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{-(-3)-\sqrt{633}}{2*-2}=\frac{3-\sqrt{633}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{633}}{2*-2}=\frac{3+\sqrt{633}}{-4}
$