3/4x+6=3x-10

Solution for 3/4x+6=3x-10 equation:

3/4x+6=3x-10

We move all terms to the left:

3/4x+6-(3x-10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-3x+10+6=0

We multiply all the terms by the denominator


-3x*4x+10*4x+6*4x+3=0

Wy multiply elements

-12x^2+40x+24x+3=0

We add all the numbers together, and all the variables

-12x^2+64x+3=0

a = -12; b = 64; c = +3;
Δ = b2-4ac
Δ = 642-4·(-12)·3
Δ = 4240
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:

$\sqrt{\Delta}=\sqrt{4240}=\sqrt{16*265}=\sqrt{16}*\sqrt{265}=4\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{265}}{2*-12}=\frac{-64-4\sqrt{265}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{265}}{2*-12}=\frac{-64+4\sqrt{265}}{-24}
$