7/2x=4x-3

Solution for 7/2x=4x-3 equation:

7/2x=4x-3

We move all terms to the left:

7/2x-(4x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7/2x-4x+3=0

We multiply all the terms by the denominator


-4x*2x+3*2x+7=0

Wy multiply elements

-8x^2+6x+7=0

a = -8; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-8)·7
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{65}}{2*-8}=\frac{-6-2\sqrt{65}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{65}}{2*-8}=\frac{-6+2\sqrt{65}}{-16}
$