-6(3x/4-2)+3=-1/2x+7

Solution for -6(3x/4-2)+3=-1/2x+7 equation:

-6(3x/4-2)+3=-1/2x+7

We move all terms to the left:

-6(3x/4-2)+3-(-1/2x+7)=0


Domain of the equation: 2x+7)!=0

x∈R


We multiply parentheses

-18x-(-1/2x+7)+12+3=0

We get rid of parentheses

-18x+1/2x-7+12+3=0

We multiply all the terms by the denominator


-18x*2x-7*2x+12*2x+3*2x+1=0

Wy multiply elements

-36x^2-14x+24x+6x+1=0

We add all the numbers together, and all the variables

-36x^2+16x+1=0

a = -36; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-36)·1
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*-36}=\frac{-36}{-72}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*-36}=\frac{4}{-72}
=-1/18
$