2/5x-2=-x+12

Solution for 2/5x-2=-x+12 equation:

2/5x-2=-x+12

We move all terms to the left:

2/5x-2-(-x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-1x+12)-2=0

We get rid of parentheses

2/5x+1x-12-2=0

We multiply all the terms by the denominator


1x*5x-12*5x-2*5x+2=0

Wy multiply elements

5x^2-60x-10x+2=0

We add all the numbers together, and all the variables

5x^2-70x+2=0

a = 5; b = -70; c = +2;
Δ = b2-4ac
Δ = -702-4·5·2
Δ = 4860
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:

$\sqrt{\Delta}=\sqrt{4860}=\sqrt{324*15}=\sqrt{324}*\sqrt{15}=18\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-18\sqrt{15}}{2*5}=\frac{70-18\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+18\sqrt{15}}{2*5}=\frac{70+18\sqrt{15}}{10}
$