8+7/10x=6x+15

Solution for 8+7/10x=6x+15 equation:

8+7/10x=6x+15

We move all terms to the left:

8+7/10x-(6x+15)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

7/10x-6x-15+8=0

We multiply all the terms by the denominator


-6x*10x-15*10x+8*10x+7=0

Wy multiply elements

-60x^2-150x+80x+7=0

We add all the numbers together, and all the variables

-60x^2-70x+7=0

a = -60; b = -70; c = +7;
Δ = b2-4ac
Δ = -702-4·(-60)·7
Δ = 6580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6580}=\sqrt{4*1645}=\sqrt{4}*\sqrt{1645}=2\sqrt{1645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1645}}{2*-60}=\frac{70-2\sqrt{1645}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1645}}{2*-60}=\frac{70+2\sqrt{1645}}{-120}
$