1/4x+6(x-0.5)=15.75

Solution for 1/4x+6(x-0.5)=15.75 equation:

1/4x+6(x-0.5)=15.75

We move all terms to the left:

1/4x+6(x-0.5)-(15.75)=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+6(x-0.5)-15.75=0

We multiply parentheses

1/4x+6x-3-15.75=0

We multiply all the terms by the denominator


6x*4x-3*4x-(15.75)*4x+1=0

We multiply parentheses

6x*4x-3*4x-63x+1=0

Wy multiply elements

24x^2-12x-63x+1=0

We add all the numbers together, and all the variables

24x^2-75x+1=0

a = 24; b = -75; c = +1;
Δ = b2-4ac
Δ = -752-4·24·1
Δ = 5529
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{-(-75)-\sqrt{5529}}{2*24}=\frac{75-\sqrt{5529}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5529}}{2*24}=\frac{75+\sqrt{5529}}{48}
$