/7x-12+5x-8=10x+14

Solution for /7x-12+5x-8=10x+14 equation:

/7x-12+5x-8=10x+14

We move all terms to the left:

/7x-12+5x-8-(10x+14)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5x+/7x-(10x+14)-20=0

We get rid of parentheses

5x+/7x-10x-14-20=0

We multiply all the terms by the denominator


5x*7x-10x*7x-14*7x-20*7x+=0

We add all the numbers together, and all the variables

5x*7x-10x*7x-14*7x-20*7x=0

Wy multiply elements

35x^2-70x^2-98x-140x=0

We add all the numbers together, and all the variables

-35x^2-238x=0

a = -35; b = -238; c = 0;
Δ = b2-4ac
Δ = -2382-4·(-35)·0
Δ = 56644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56644}=238$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-238)-238}{2*-35}=\frac{0}{-70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-238)+238}{2*-35}=\frac{476}{-70}
=-6+4/5
$