7/10x=6-3x

Solution for 7/10x=6-3x equation:

7/10x=6-3x

We move all terms to the left:

7/10x-(6-3x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

7/10x-(-3x+6)=0

We get rid of parentheses

7/10x+3x-6=0

We multiply all the terms by the denominator


3x*10x-6*10x+7=0

Wy multiply elements

30x^2-60x+7=0

a = 30; b = -60; c = +7;
Δ = b2-4ac
Δ = -602-4·30·7
Δ = 2760
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:

$\sqrt{\Delta}=\sqrt{2760}=\sqrt{4*690}=\sqrt{4}*\sqrt{690}=2\sqrt{690}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{690}}{2*30}=\frac{60-2\sqrt{690}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{690}}{2*30}=\frac{60+2\sqrt{690}}{60}
$