6/5x+10+7/6x+12=0

Solution for 6/5x+10+7/6x+12=0 equation:

6/5x+10+7/6x+12=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

6/5x+7/6x+22=0

We calculate fractions


36x/30x^2+35x/30x^2+22=0

We multiply all the terms by the denominator


36x+35x+22*30x^2=0

We add all the numbers together, and all the variables

71x+22*30x^2=0

Wy multiply elements

660x^2+71x=0

a = 660; b = 71; c = 0;
Δ = b2-4ac
Δ = 712-4·660·0
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(71)-71}{2*660}=\frac{-142}{1320}
=-71/660
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+71}{2*660}=\frac{0}{1320}
=0
$