5x=3/2x+42

Solution for 5x=3/2x+42 equation:

5x=3/2x+42

We move all terms to the left:

5x-(3/2x+42)=0


Domain of the equation: 2x+42)!=0

x∈R


We get rid of parentheses

5x-3/2x-42=0

We multiply all the terms by the denominator


5x*2x-42*2x-3=0

Wy multiply elements

10x^2-84x-3=0

a = 10; b = -84; c = -3;
Δ = b2-4ac
Δ = -842-4·10·(-3)
Δ = 7176
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:

$\sqrt{\Delta}=\sqrt{7176}=\sqrt{4*1794}=\sqrt{4}*\sqrt{1794}=2\sqrt{1794}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1794}}{2*10}=\frac{84-2\sqrt{1794}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1794}}{2*10}=\frac{84+2\sqrt{1794}}{20}
$