(3/4x+6)=2x-5

Solution for (3/4x+6)=2x-5 equation:

(3/4x+6)=2x-5

We move all terms to the left:

(3/4x+6)-(2x-5)=0


Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

3/4x-2x+6+5=0

We multiply all the terms by the denominator


-2x*4x+6*4x+5*4x+3=0

Wy multiply elements

-8x^2+24x+20x+3=0

We add all the numbers together, and all the variables

-8x^2+44x+3=0

a = -8; b = 44; c = +3;
Δ = b2-4ac
Δ = 442-4·(-8)·3
Δ = 2032
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:

$\sqrt{\Delta}=\sqrt{2032}=\sqrt{16*127}=\sqrt{16}*\sqrt{127}=4\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{127}}{2*-8}=\frac{-44-4\sqrt{127}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{127}}{2*-8}=\frac{-44+4\sqrt{127}}{-16}
$