3/2x+5=7x

Solution for 3/2x+5=7x equation:

3/2x+5=7x

We move all terms to the left:

3/2x+5-(7x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+3/2x+5=0

We multiply all the terms by the denominator


-7x*2x+5*2x+3=0

Wy multiply elements

-14x^2+10x+3=0

a = -14; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-14)·3
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{67}}{2*-14}=\frac{-10-2\sqrt{67}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{67}}{2*-14}=\frac{-10+2\sqrt{67}}{-28}
$