4/5z+2=7/10z+8

Solution for 4/5z+2=7/10z+8 equation:

4/5z+2=7/10z+8

We move all terms to the left:

4/5z+2-(7/10z+8)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 10z+8)!=0

z∈R


We get rid of parentheses

4/5z-7/10z-8+2=0

We calculate fractions


40z/50z^2+(-35z)/50z^2-8+2=0

We add all the numbers together, and all the variables

40z/50z^2+(-35z)/50z^2-6=0

We multiply all the terms by the denominator


40z+(-35z)-6*50z^2=0

Wy multiply elements

-300z^2+40z+(-35z)=0

We get rid of parentheses

-300z^2+40z-35z=0

We add all the numbers together, and all the variables

-300z^2+5z=0

a = -300; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-300)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-300}=\frac{-10}{-600}
=1/60
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-300}=\frac{0}{-600}
=0
$