3/4x+6=12-7x

Solution for 3/4x+6=12-7x equation:

3/4x+6=12-7x

We move all terms to the left:

3/4x+6-(12-7x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-7x+12)+6=0

We get rid of parentheses

3/4x+7x-12+6=0

We multiply all the terms by the denominator


7x*4x-12*4x+6*4x+3=0

Wy multiply elements

28x^2-48x+24x+3=0

We add all the numbers together, and all the variables

28x^2-24x+3=0

a = 28; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·28·3
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{15}}{2*28}=\frac{24-4\sqrt{15}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{15}}{2*28}=\frac{24+4\sqrt{15}}{56}
$