1/2x=x-37

Solution for 1/2x=x-37 equation:

1/2x=x-37

We move all terms to the left:

1/2x-(x-37)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x+37=0

We multiply all the terms by the denominator


-x*2x+37*2x+1=0

Wy multiply elements

-2x^2+74x+1=0

a = -2; b = 74; c = +1;
Δ = b2-4ac
Δ = 742-4·(-2)·1
Δ = 5484
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:

$\sqrt{\Delta}=\sqrt{5484}=\sqrt{4*1371}=\sqrt{4}*\sqrt{1371}=2\sqrt{1371}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-2\sqrt{1371}}{2*-2}=\frac{-74-2\sqrt{1371}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+2\sqrt{1371}}{2*-2}=\frac{-74+2\sqrt{1371}}{-4}
$