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

Solution for 4x+(6/2x-3)-7=0 equation:

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


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

4x+6/2x-3-7=0

We multiply all the terms by the denominator


4x*2x-3*2x-7*2x+6=0

Wy multiply elements

8x^2-6x-14x+6=0

We add all the numbers together, and all the variables

8x^2-20x+6=0

a = 8; b = -20; c = +6;
Δ = b2-4ac
Δ = -202-4·8·6
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{13}}{2*8}=\frac{20-4\sqrt{13}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{13}}{2*8}=\frac{20+4\sqrt{13}}{16}
$