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

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

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

We move all terms to the left:

1/2a-3+3/4a-(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

1/2a+3/4a-10=0

We calculate fractions


4a/8a^2+6a/8a^2-10=0

We multiply all the terms by the denominator


4a+6a-10*8a^2=0

We add all the numbers together, and all the variables

10a-10*8a^2=0

Wy multiply elements

-80a^2+10a=0

a = -80; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-80)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-80}=\frac{-20}{-160}
=1/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-80}=\frac{0}{-160}
=0
$