X-15/2x=83

Solution for X-15/2x=83 equation:

X-15/2X=83

We move all terms to the left:

X-15/2X-(83)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-83*2X-15=0

Wy multiply elements

2X^2-166X-15=0

a = 2; b = -166; c = -15;
Δ = b2-4ac
Δ = -1662-4·2·(-15)
Δ = 27676
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:

$\sqrt{\Delta}=\sqrt{27676}=\sqrt{4*6919}=\sqrt{4}*\sqrt{6919}=2\sqrt{6919}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-2\sqrt{6919}}{2*2}=\frac{166-2\sqrt{6919}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+2\sqrt{6919}}{2*2}=\frac{166+2\sqrt{6919}}{4}
$