1/4x-2=-6+5x

Solution for 1/4x-2=-6+5x equation:

1/4x-2=-6+5x

We move all terms to the left:

1/4x-2-(-6+5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(5x-6)-2=0

We get rid of parentheses

1/4x-5x+6-2=0

We multiply all the terms by the denominator


-5x*4x+6*4x-2*4x+1=0

Wy multiply elements

-20x^2+24x-8x+1=0

We add all the numbers together, and all the variables

-20x^2+16x+1=0

a = -20; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-20)·1
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{21}}{2*-20}=\frac{-16-4\sqrt{21}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{21}}{2*-20}=\frac{-16+4\sqrt{21}}{-40}
$