6a-3a/2a=10-2+7

Solution for 6a-3a/2a=10-2+7 equation:

6a-3a/2a=10-2+7

We move all terms to the left:

6a-3a/2a-(10-2+7)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

6a-3a/2a-15=0

We multiply all the terms by the denominator


6a*2a-3a-15*2a=0

We add all the numbers together, and all the variables

-3a+6a*2a-15*2a=0

Wy multiply elements

12a^2-3a-30a=0

We add all the numbers together, and all the variables

12a^2-33a=0

a = 12; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·12·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*12}=\frac{0}{24}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*12}=\frac{66}{24}
=2+3/4
$