4(3+2x)-7=7/2x+14

Solution for 4(3+2x)-7=7/2x+14 equation:

4(3+2x)-7=7/2x+14

We move all terms to the left:

4(3+2x)-7-(7/2x+14)=0


Domain of the equation: 2x+14)!=0

x∈R


We add all the numbers together, and all the variables

4(2x+3)-(7/2x+14)-7=0

We multiply parentheses

8x-(7/2x+14)+12-7=0

We get rid of parentheses

8x-7/2x-14+12-7=0

We multiply all the terms by the denominator


8x*2x-14*2x+12*2x-7*2x-7=0

Wy multiply elements

16x^2-28x+24x-14x-7=0

We add all the numbers together, and all the variables

16x^2-18x-7=0

a = 16; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·16·(-7)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{193}}{2*16}=\frac{18-2\sqrt{193}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{193}}{2*16}=\frac{18+2\sqrt{193}}{32}
$