-4x+5=14/3x-20

Solution for -4x+5=14/3x-20 equation:

-4x+5=14/3x-20

We move all terms to the left:

-4x+5-(14/3x-20)=0


Domain of the equation: 3x-20)!=0

x∈R


We get rid of parentheses

-4x-14/3x+20+5=0

We multiply all the terms by the denominator


-4x*3x+20*3x+5*3x-14=0

Wy multiply elements

-12x^2+60x+15x-14=0

We add all the numbers together, and all the variables

-12x^2+75x-14=0

a = -12; b = 75; c = -14;
Δ = b2-4ac
Δ = 752-4·(-12)·(-14)
Δ = 4953
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-\sqrt{4953}}{2*-12}=\frac{-75-\sqrt{4953}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{4953}}{2*-12}=\frac{-75+\sqrt{4953}}{-24}
$