.4x+10=1/5x+12

Solution for .4x+10=1/5x+12 equation:

.4x+10=1/5x+12

We move all terms to the left:

.4x+10-(1/5x+12)=0


Domain of the equation: 5x+12)!=0

x∈R


We get rid of parentheses

.4x-1/5x-12+10=0

We multiply all the terms by the denominator


(.4x)*5x-12*5x+10*5x-1=0

We add all the numbers together, and all the variables

(+.4x)*5x-12*5x+10*5x-1=0

We multiply parentheses

5x^2-12*5x+10*5x-1=0

Wy multiply elements

5x^2-60x+50x-1=0

We add all the numbers together, and all the variables

5x^2-10x-1=0

a = 5; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·5·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{30}}{2*5}=\frac{10-2\sqrt{30}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{30}}{2*5}=\frac{10+2\sqrt{30}}{10}
$