11x=21/2x+12

Solution for 11x=21/2x+12 equation:

11x=21/2x+12

We move all terms to the left:

11x-(21/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

11x-21/2x-12=0

We multiply all the terms by the denominator


11x*2x-12*2x-21=0

Wy multiply elements

22x^2-24x-21=0

a = 22; b = -24; c = -21;
Δ = b2-4ac
Δ = -242-4·22·(-21)
Δ = 2424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{606}}{2*22}=\frac{24-2\sqrt{606}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{606}}{2*22}=\frac{24+2\sqrt{606}}{44}
$