7x-3/2x+3=0

Solution for 7x-3/2x+3=0 equation:

7x-3/2x+3=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

14x^2+6x-3=0

a = 14; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·14·(-3)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{51}}{2*14}=\frac{-6-2\sqrt{51}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{51}}{2*14}=\frac{-6+2\sqrt{51}}{28}
$