7/10x+5/6x=15

Solution for 7/10x+5/6x=15 equation:

7/10x+5/6x=15

We move all terms to the left:

7/10x+5/6x-(15)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


42x/60x^2+50x/60x^2-15=0

We multiply all the terms by the denominator


42x+50x-15*60x^2=0

We add all the numbers together, and all the variables

92x-15*60x^2=0

Wy multiply elements

-900x^2+92x=0

a = -900; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·(-900)·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*-900}=\frac{-184}{-1800}
=23/225
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*-900}=\frac{0}{-1800}
=0
$