7/2x=5x-10

Solution for 7/2x=5x-10 equation:

7/2x=5x-10

We move all terms to the left:

7/2x-(5x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7/2x-5x+10=0

We multiply all the terms by the denominator


-5x*2x+10*2x+7=0

Wy multiply elements

-10x^2+20x+7=0

a = -10; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·(-10)·7
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{170}}{2*-10}=\frac{-20-2\sqrt{170}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{170}}{2*-10}=\frac{-20+2\sqrt{170}}{-20}
$