x=1001/2x-35

Solution for x=1001/2x-35 equation:

x=1001/2x-35

We move all terms to the left:

x-(1001/2x-35)=0


Domain of the equation: 2x-35)!=0

x∈R


We get rid of parentheses

x-1001/2x+35=0

We multiply all the terms by the denominator


x*2x+35*2x-1001=0

Wy multiply elements

2x^2+70x-1001=0

a = 2; b = 70; c = -1001;
Δ = b2-4ac
Δ = 702-4·2·(-1001)
Δ = 12908
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:

$\sqrt{\Delta}=\sqrt{12908}=\sqrt{4*3227}=\sqrt{4}*\sqrt{3227}=2\sqrt{3227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{3227}}{2*2}=\frac{-70-2\sqrt{3227}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{3227}}{2*2}=\frac{-70+2\sqrt{3227}}{4}
$