((6/5)x^2)-(5x)=0

Solution for ((6/5)x^2)-(5x)=0 equation:

((6/5)x^2)-(5x)=0


Domain of the equation: 5)x^2)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

((+6/5)x^2)-5x=0

We add all the numbers together, and all the variables

-5x+((+6/5)x^2)=0

We multiply all the terms by the denominator


-5x*5)x^2)+((+6=0

Wy multiply elements

-25x^2+6=0

a = -25; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-25)·6
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-25}=\frac{0-10\sqrt{6}}{-50}
=-\frac{10\sqrt{6}}{-50}
=-\frac{\sqrt{6}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-25}=\frac{0+10\sqrt{6}}{-50}
=\frac{10\sqrt{6}}{-50}
=\frac{\sqrt{6}}{-5}
$