7/x+5+8/3x+15=10

Solution for 7/x+5+8/3x+15=10 equation:

7/x+5+8/3x+15=10

We move all terms to the left:

7/x+5+8/3x+15-(10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7/x+8/3x+10=0

We calculate fractions


21x/3x^2+8x/3x^2+10=0

We multiply all the terms by the denominator


21x+8x+10*3x^2=0

We add all the numbers together, and all the variables

29x+10*3x^2=0

Wy multiply elements

30x^2+29x=0

a = 30; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·30·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*30}=\frac{-58}{60}
=-29/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*30}=\frac{0}{60}
=0
$