2/5x=4x-7

Solution for 2/5x=4x-7 equation:

2/5x=4x-7

We move all terms to the left:

2/5x-(4x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-4x+7=0

We multiply all the terms by the denominator


-4x*5x+7*5x+2=0

Wy multiply elements

-20x^2+35x+2=0

a = -20; b = 35; c = +2;
Δ = b2-4ac
Δ = 352-4·(-20)·2
Δ = 1385
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{-(35)-\sqrt{1385}}{2*-20}=\frac{-35-\sqrt{1385}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1385}}{2*-20}=\frac{-35+\sqrt{1385}}{-40}
$