35x-21/2x=65

Solution for 35x-21/2x=65 equation:

35x-21/2x=65

We move all terms to the left:

35x-21/2x-(65)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


35x*2x-65*2x-21=0

Wy multiply elements

70x^2-130x-21=0

a = 70; b = -130; c = -21;
Δ = b2-4ac
Δ = -1302-4·70·(-21)
Δ = 22780
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:

$\sqrt{\Delta}=\sqrt{22780}=\sqrt{4*5695}=\sqrt{4}*\sqrt{5695}=2\sqrt{5695}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{5695}}{2*70}=\frac{130-2\sqrt{5695}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{5695}}{2*70}=\frac{130+2\sqrt{5695}}{140}
$