6x-20=3/4x-7

Solution for 6x-20=3/4x-7 equation:

6x-20=3/4x-7

We move all terms to the left:

6x-20-(3/4x-7)=0


Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

6x-3/4x+7-20=0

We multiply all the terms by the denominator


6x*4x+7*4x-20*4x-3=0

Wy multiply elements

24x^2+28x-80x-3=0

We add all the numbers together, and all the variables

24x^2-52x-3=0

a = 24; b = -52; c = -3;
Δ = b2-4ac
Δ = -522-4·24·(-3)
Δ = 2992
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:

$\sqrt{\Delta}=\sqrt{2992}=\sqrt{16*187}=\sqrt{16}*\sqrt{187}=4\sqrt{187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{187}}{2*24}=\frac{52-4\sqrt{187}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{187}}{2*24}=\frac{52+4\sqrt{187}}{48}
$