5/6x+15/8x=8

Solution for 5/6x+15/8x=8 equation:

5/6x+15/8x=8

We move all terms to the left:

5/6x+15/8x-(8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


40x/48x^2+90x/48x^2-8=0

We multiply all the terms by the denominator


40x+90x-8*48x^2=0

We add all the numbers together, and all the variables

130x-8*48x^2=0

Wy multiply elements

-384x^2+130x=0

a = -384; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·(-384)·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*-384}=\frac{-260}{-768}
=65/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*-384}=\frac{0}{-768}
=0
$