38=3/2y+23y=

Solution for 38=3/2y+23y= equation:

38=3/2y+23y=

We move all terms to the left:

38-(3/2y+23y)=0


Domain of the equation: 2y+23y)!=0

y∈R


We add all the numbers together, and all the variables

-(+23y+3/2y)+38=0

We get rid of parentheses

-23y-3/2y+38=0

We multiply all the terms by the denominator


-23y*2y+38*2y-3=0

Wy multiply elements

-46y^2+76y-3=0

a = -46; b = 76; c = -3;
Δ = b2-4ac
Δ = 762-4·(-46)·(-3)
Δ = 5224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5224}=\sqrt{4*1306}=\sqrt{4}*\sqrt{1306}=2\sqrt{1306}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{1306}}{2*-46}=\frac{-76-2\sqrt{1306}}{-92}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{1306}}{2*-46}=\frac{-76+2\sqrt{1306}}{-92}
$