7x=21/2x+7

Solution for 7x=21/2x+7 equation:

7x=21/2x+7

We move all terms to the left:

7x-(21/2x+7)=0


Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

7x-21/2x-7=0

We multiply all the terms by the denominator


7x*2x-7*2x-21=0

Wy multiply elements

14x^2-14x-21=0

a = 14; b = -14; c = -21;
Δ = b2-4ac
Δ = -142-4·14·(-21)
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{7}}{2*14}=\frac{14-14\sqrt{7}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{7}}{2*14}=\frac{14+14\sqrt{7}}{28}
$