7+5/3x=4x-14

Solution for 7+5/3x=4x-14 equation:

7+5/3x=4x-14

We move all terms to the left:

7+5/3x-(4x-14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

5/3x-4x+14+7=0

We multiply all the terms by the denominator


-4x*3x+14*3x+7*3x+5=0

Wy multiply elements

-12x^2+42x+21x+5=0

We add all the numbers together, and all the variables

-12x^2+63x+5=0

a = -12; b = 63; c = +5;
Δ = b2-4ac
Δ = 632-4·(-12)·5
Δ = 4209
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{-(63)-\sqrt{4209}}{2*-12}=\frac{-63-\sqrt{4209}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+\sqrt{4209}}{2*-12}=\frac{-63+\sqrt{4209}}{-24}
$