(10/4x)+3=2x-3

Solution for (10/4x)+3=2x-3 equation:

(10/4x)+3=2x-3

We move all terms to the left:

(10/4x)+3-(2x-3)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+10/4x)-(2x-3)+3=0

We get rid of parentheses

10/4x-2x+3+3=0

We multiply all the terms by the denominator


-2x*4x+3*4x+3*4x+10=0

Wy multiply elements

-8x^2+12x+12x+10=0

We add all the numbers together, and all the variables

-8x^2+24x+10=0

a = -8; b = 24; c = +10;
Δ = b2-4ac
Δ = 242-4·(-8)·10
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{14}}{2*-8}=\frac{-24-8\sqrt{14}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{14}}{2*-8}=\frac{-24+8\sqrt{14}}{-16}
$