10/4x-20=4x-3

Solution for 10/4x-20=4x-3 equation:

10/4x-20=4x-3

We move all terms to the left:

10/4x-20-(4x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

10/4x-4x+3-20=0

We multiply all the terms by the denominator


-4x*4x+3*4x-20*4x+10=0

Wy multiply elements

-16x^2+12x-80x+10=0

We add all the numbers together, and all the variables

-16x^2-68x+10=0

a = -16; b = -68; c = +10;
Δ = b2-4ac
Δ = -682-4·(-16)·10
Δ = 5264
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:

$\sqrt{\Delta}=\sqrt{5264}=\sqrt{16*329}=\sqrt{16}*\sqrt{329}=4\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{329}}{2*-16}=\frac{68-4\sqrt{329}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{329}}{2*-16}=\frac{68+4\sqrt{329}}{-32}
$