x+61=1/2x+22

Solution for x+61=1/2x+22 equation:

x+61=1/2x+22

We move all terms to the left:

x+61-(1/2x+22)=0


Domain of the equation: 2x+22)!=0

x∈R


We get rid of parentheses

x-1/2x-22+61=0

We multiply all the terms by the denominator


x*2x-22*2x+61*2x-1=0

Wy multiply elements

2x^2-44x+122x-1=0

We add all the numbers together, and all the variables

2x^2+78x-1=0

a = 2; b = 78; c = -1;
Δ = b2-4ac
Δ = 782-4·2·(-1)
Δ = 6092
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:

$\sqrt{\Delta}=\sqrt{6092}=\sqrt{4*1523}=\sqrt{4}*\sqrt{1523}=2\sqrt{1523}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1523}}{2*2}=\frac{-78-2\sqrt{1523}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1523}}{2*2}=\frac{-78+2\sqrt{1523}}{4}
$