5(x+2)/2x-14=X=10

Solution for 5(x+2)/2x-14=X=10 equation:

5(x+2)/2x-14=x=10

We move all terms to the left:

5(x+2)/2x-14-(x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5(x+2)/2x-14=0

We multiply all the terms by the denominator


-1x*2x+5(x+2)-14*2x=0

We multiply parentheses

-1x*2x+5x-14*2x+10=0

Wy multiply elements

-2x^2+5x-28x+10=0

We add all the numbers together, and all the variables

-2x^2-23x+10=0

a = -2; b = -23; c = +10;
Δ = b2-4ac
Δ = -232-4·(-2)·10
Δ = 609
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{-(-23)-\sqrt{609}}{2*-2}=\frac{23-\sqrt{609}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{609}}{2*-2}=\frac{23+\sqrt{609}}{-4}
$