3-2/9l=1/3l-7

Solution for 3-2/9l=1/3l-7 equation:

3-2/9l=1/3l-7

We move all terms to the left:

3-2/9l-(1/3l-7)=0


Domain of the equation: 9l!=0

l!=0/9

l!=0

l∈R



Domain of the equation: 3l-7)!=0

l∈R


We get rid of parentheses

-2/9l-1/3l+7+3=0

We calculate fractions


(-6l)/27l^2+(-9l)/27l^2+7+3=0

We add all the numbers together, and all the variables

(-6l)/27l^2+(-9l)/27l^2+10=0

We multiply all the terms by the denominator


(-6l)+(-9l)+10*27l^2=0

Wy multiply elements

270l^2+(-6l)+(-9l)=0

We get rid of parentheses

270l^2-6l-9l=0

We add all the numbers together, and all the variables

270l^2-15l=0

a = 270; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·270·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*270}=\frac{0}{540}
=0
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*270}=\frac{30}{540}
=1/18
$