7/2x=4+10x

Solution for 7/2x=4+10x equation:

7/2x=4+10x

We move all terms to the left:

7/2x-(4+10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-(10x+4)=0

We get rid of parentheses

7/2x-10x-4=0

We multiply all the terms by the denominator


-10x*2x-4*2x+7=0

Wy multiply elements

-20x^2-8x+7=0

a = -20; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-20)·7
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{39}}{2*-20}=\frac{8-4\sqrt{39}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{39}}{2*-20}=\frac{8+4\sqrt{39}}{-40}
$