Y=-4/15x+24x=120

Solution for Y=-4/15x+24x=120 equation:

=-4/15Y+24Y=120

We move all terms to the left:

-(-4/15Y+24Y)=0


Domain of the equation: 15Y+24Y)!=0

Y∈R


We add all the numbers together, and all the variables

-(+24Y-4/15Y)=0

We get rid of parentheses

-24Y+4/15Y=0

We multiply all the terms by the denominator


-24Y*15Y+4=0

Wy multiply elements

-360Y^2+4=0

a = -360; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-360)·4
Δ = 5760
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{10}}{2*-360}=\frac{0-24\sqrt{10}}{-720}
=-\frac{24\sqrt{10}}{-720}
=-\frac{\sqrt{10}}{-30}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{10}}{2*-360}=\frac{0+24\sqrt{10}}{-720}
=\frac{24\sqrt{10}}{-720}
=\frac{\sqrt{10}}{-30}
$