4/5x+3/2x=12

Solution for 4/5x+3/2x=12 equation:

4/5x+3/2x=12

We move all terms to the left:

4/5x+3/2x-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


8x/10x^2+15x/10x^2-12=0

We multiply all the terms by the denominator


8x+15x-12*10x^2=0

We add all the numbers together, and all the variables

23x-12*10x^2=0

Wy multiply elements

-120x^2+23x=0

a = -120; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-120)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-120}=\frac{-46}{-240}
=23/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-120}=\frac{0}{-240}
=0
$