(2/5x-1)(4x-5)=0

Solution for (2/5x-1)(4x-5)=0 equation:

(2/5x-1)(4x-5)=0


Domain of the equation: 5x-1)(4x-5)!=0

x∈R


We multiply parentheses ..

(+8x^2-10x-4x+5)=0

We get rid of parentheses

8x^2-10x-4x+5=0

We add all the numbers together, and all the variables

8x^2-14x+5=0

a = 8; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·8·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*8}=\frac{8}{16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*8}=\frac{20}{16}
=1+1/4
$