3/4x+7=4x-12

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

3/4x+7=4x-12

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2+48x+28x+3=0

We add all the numbers together, and all the variables

-16x^2+76x+3=0

a = -16; b = 76; c = +3;
Δ = b2-4ac
Δ = 762-4·(-16)·3
Δ = 5968
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:

$\sqrt{\Delta}=\sqrt{5968}=\sqrt{16*373}=\sqrt{16}*\sqrt{373}=4\sqrt{373}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-4\sqrt{373}}{2*-16}=\frac{-76-4\sqrt{373}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+4\sqrt{373}}{2*-16}=\frac{-76+4\sqrt{373}}{-32}
$