-4z-3/5z+6=-5/5z+6

Solution for -4z-3/5z+6=-5/5z+6 equation:

-4z-3/5z+6=-5/5z+6

We move all terms to the left:

-4z-3/5z+6-(-5/5z+6)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 5z+6)!=0

z∈R


We get rid of parentheses

-4z-3/5z+5/5z-6+6=0

We multiply all the terms by the denominator


-4z*5z-6*5z+6*5z-3+5=0

We add all the numbers together, and all the variables

-4z*5z-6*5z+6*5z+2=0

Wy multiply elements

-20z^2-30z+30z+2=0

We add all the numbers together, and all the variables

-20z^2+2=0

a = -20; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-20)·2
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-20}=\frac{0-4\sqrt{10}}{-40}
=-\frac{4\sqrt{10}}{-40}
=-\frac{\sqrt{10}}{-10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-20}=\frac{0+4\sqrt{10}}{-40}
=\frac{4\sqrt{10}}{-40}
=\frac{\sqrt{10}}{-10}
$