3a-7/a-10=1

Solution for 3a-7/a-10=1 equation:

3a-7/a-10=1

We move all terms to the left:

3a-7/a-10-(1)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

3a-7/a-11=0

We multiply all the terms by the denominator


3a*a-11*a-7=0

We add all the numbers together, and all the variables

-11a+3a*a-7=0

Wy multiply elements

3a^2-11a-7=0

a = 3; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·3·(-7)
Δ = 205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{205}}{2*3}=\frac{11-\sqrt{205}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{205}}{2*3}=\frac{11+\sqrt{205}}{6}
$