3/2a+1/4a-8=7

Solution for 3/2a+1/4a-8=7 equation:

3/2a+1/4a-8=7

We move all terms to the left:

3/2a+1/4a-8-(7)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

3/2a+1/4a-15=0

We calculate fractions


12a/8a^2+2a/8a^2-15=0

We multiply all the terms by the denominator


12a+2a-15*8a^2=0

We add all the numbers together, and all the variables

14a-15*8a^2=0

Wy multiply elements

-120a^2+14a=0

a = -120; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-120)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-120}=\frac{-28}{-240}
=7/60
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-120}=\frac{0}{-240}
=0
$