7x-3=4+3/2x

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

7x-3=4+3/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

14x^2-8x-6x-3=0

We add all the numbers together, and all the variables

14x^2-14x-3=0

a = 14; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·14·(-3)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{91}}{2*14}=\frac{14-2\sqrt{91}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{91}}{2*14}=\frac{14+2\sqrt{91}}{28}
$