2x-14/5x-9=4x+1

Solution for 2x-14/5x-9=4x+1 equation:

2x-14/5x-9=4x+1

We move all terms to the left:

2x-14/5x-9-(4x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2x-14/5x-4x-1-9=0

We multiply all the terms by the denominator


2x*5x-4x*5x-1*5x-9*5x-14=0

Wy multiply elements

10x^2-20x^2-5x-45x-14=0

We add all the numbers together, and all the variables

-10x^2-50x-14=0

a = -10; b = -50; c = -14;
Δ = b2-4ac
Δ = -502-4·(-10)·(-14)
Δ = 1940
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:

$\sqrt{\Delta}=\sqrt{1940}=\sqrt{4*485}=\sqrt{4}*\sqrt{485}=2\sqrt{485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{485}}{2*-10}=\frac{50-2\sqrt{485}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{485}}{2*-10}=\frac{50+2\sqrt{485}}{-20}
$