14+5/7x-20=4.7x-4

Solution for 14+5/7x-20=4.7x-4 equation:

14+5/7x-20=4.7x-4

We move all terms to the left:

14+5/7x-20-(4.7x-4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5/7x-(4.7x-4)-6=0

We get rid of parentheses

5/7x-4.7x+4-6=0

We multiply all the terms by the denominator


-(4.7x)*7x+4*7x-6*7x+5=0

We add all the numbers together, and all the variables

-(+4.7x)*7x+4*7x-6*7x+5=0

We multiply parentheses

-28x^2+4*7x-6*7x+5=0

Wy multiply elements

-28x^2+28x-42x+5=0

We add all the numbers together, and all the variables

-28x^2-14x+5=0

a = -28; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·(-28)·5
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{21}}{2*-28}=\frac{14-6\sqrt{21}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{21}}{2*-28}=\frac{14+6\sqrt{21}}{-56}
$