65/100l=l-70

Solution for 65/100l=l-70 equation:

65/100l=l-70

We move all terms to the left:

65/100l-(l-70)=0


Domain of the equation: 100l!=0

l!=0/100

l!=0

l∈R


We get rid of parentheses

65/100l-l+70=0

We multiply all the terms by the denominator


-l*100l+70*100l+65=0

Wy multiply elements

-100l^2+7000l+65=0

a = -100; b = 7000; c = +65;
Δ = b2-4ac
Δ = 70002-4·(-100)·65
Δ = 49026000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{49026000}=\sqrt{400*122565}=\sqrt{400}*\sqrt{122565}=20\sqrt{122565}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7000)-20\sqrt{122565}}{2*-100}=\frac{-7000-20\sqrt{122565}}{-200}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7000)+20\sqrt{122565}}{2*-100}=\frac{-7000+20\sqrt{122565}}{-200}
$