(-3/4)z+1=-41/70

Solution for (-3/4)z+1=-41/70 equation:

(-3/4)z+1=-41/70

We move all terms to the left:

(-3/4)z+1-(-41/70)=0


Domain of the equation: 4)z!=0

z!=0/1

z!=0

z∈R


We multiply parentheses

-3z^2+1-(-41/70)=0

We get rid of parentheses

-3z^2+1+41/70=0

We multiply all the terms by the denominator


-3z^2*70+41+1*70=0

We add all the numbers together, and all the variables

-3z^2*70+111=0

Wy multiply elements

-210z^2+111=0

a = -210; b = 0; c = +111;
Δ = b2-4ac
Δ = 02-4·(-210)·111
Δ = 93240
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:

$\sqrt{\Delta}=\sqrt{93240}=\sqrt{36*2590}=\sqrt{36}*\sqrt{2590}=6\sqrt{2590}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2590}}{2*-210}=\frac{0-6\sqrt{2590}}{-420}
=-\frac{6\sqrt{2590}}{-420}
=-\frac{\sqrt{2590}}{-70}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2590}}{2*-210}=\frac{0+6\sqrt{2590}}{-420}
=\frac{6\sqrt{2590}}{-420}
=\frac{\sqrt{2590}}{-70}
$