41/10a-11=4a-12

Solution for 41/10a-11=4a-12 equation:

41/10a-11=4a-12

We move all terms to the left:

41/10a-11-(4a-12)=0


Domain of the equation: 10a!=0

a!=0/10

a!=0

a∈R


We get rid of parentheses

41/10a-4a+12-11=0

We multiply all the terms by the denominator


-4a*10a+12*10a-11*10a+41=0

Wy multiply elements

-40a^2+120a-110a+41=0

We add all the numbers together, and all the variables

-40a^2+10a+41=0

a = -40; b = 10; c = +41;
Δ = b2-4ac
Δ = 102-4·(-40)·41
Δ = 6660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6660}=\sqrt{36*185}=\sqrt{36}*\sqrt{185}=6\sqrt{185}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{185}}{2*-40}=\frac{-10-6\sqrt{185}}{-80}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{185}}{2*-40}=\frac{-10+6\sqrt{185}}{-80}
$