3/4x-5=3x-16

Solution for 3/4x-5=3x-16 equation:

3/4x-5=3x-16

We move all terms to the left:

3/4x-5-(3x-16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-3x+16-5=0

We multiply all the terms by the denominator


-3x*4x+16*4x-5*4x+3=0

Wy multiply elements

-12x^2+64x-20x+3=0

We add all the numbers together, and all the variables

-12x^2+44x+3=0

a = -12; b = 44; c = +3;
Δ = b2-4ac
Δ = 442-4·(-12)·3
Δ = 2080
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:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{130}}{2*-12}=\frac{-44-4\sqrt{130}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{130}}{2*-12}=\frac{-44+4\sqrt{130}}{-24}
$