x=3/2x+14

Solution for x=3/2x+14 equation:

x=3/2x+14

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-3/2x-14=0

We multiply all the terms by the denominator


x*2x-14*2x-3=0

Wy multiply elements

2x^2-28x-3=0

a = 2; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·2·(-3)
Δ = 808
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:

$\sqrt{\Delta}=\sqrt{808}=\sqrt{4*202}=\sqrt{4}*\sqrt{202}=2\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{202}}{2*2}=\frac{28-2\sqrt{202}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{202}}{2*2}=\frac{28+2\sqrt{202}}{4}
$