1.1-(5x-2)=1/4x-12

Solution for 1.1-(5x-2)=1/4x-12 equation:

1.1-(5x-2)=1/4x-12

We move all terms to the left:

1.1-(5x-2)-(1/4x-12)=0


Domain of the equation: 4x-12)!=0

x∈R


We get rid of parentheses

-5x-1/4x+2+12+1.1=0

We multiply all the terms by the denominator


-5x*4x+2*4x+12*4x+(1.1)*4x-1=0

We multiply parentheses

-5x*4x+2*4x+12*4x+4.4x-1=0

Wy multiply elements

-20x^2+8x+48x+4.4x-1=0

We add all the numbers together, and all the variables

-20x^2+60.4x-1=0

a = -20; b = 60.4; c = -1;
Δ = b2-4ac
Δ = 60.42-4·(-20)·(-1)
Δ = 3568.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60.4)-\sqrt{3568.16}}{2*-20}=\frac{-60.4-\sqrt{3568.16}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60.4)+\sqrt{3568.16}}{2*-20}=\frac{-60.4+\sqrt{3568.16}}{-40}
$