4/5x=2x-14

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

4/5x=2x-14

We move all terms to the left:

4/5x-(2x-14)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-2x+14=0

We multiply all the terms by the denominator


-2x*5x+14*5x+4=0

Wy multiply elements

-10x^2+70x+4=0

a = -10; b = 70; c = +4;
Δ = b2-4ac
Δ = 702-4·(-10)·4
Δ = 5060
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:

$\sqrt{\Delta}=\sqrt{5060}=\sqrt{4*1265}=\sqrt{4}*\sqrt{1265}=2\sqrt{1265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1265}}{2*-10}=\frac{-70-2\sqrt{1265}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1265}}{2*-10}=\frac{-70+2\sqrt{1265}}{-20}
$