x+7/2*x=22

Solution for x+7/2*x=22 equation:

x+7/2x=22

We move all terms to the left:

x+7/2x-(22)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-22*2x+7=0

Wy multiply elements

2x^2-44x+7=0

a = 2; b = -44; c = +7;
Δ = b2-4ac
Δ = -442-4·2·7
Δ = 1880
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:

$\sqrt{\Delta}=\sqrt{1880}=\sqrt{4*470}=\sqrt{4}*\sqrt{470}=2\sqrt{470}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{470}}{2*2}=\frac{44-2\sqrt{470}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{470}}{2*2}=\frac{44+2\sqrt{470}}{4}
$