1/2z-25=-7z-10

Solution for 1/2z-25=-7z-10 equation:

1/2z-25=-7z-10

We move all terms to the left:

1/2z-25-(-7z-10)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We get rid of parentheses

1/2z+7z+10-25=0

We multiply all the terms by the denominator


7z*2z+10*2z-25*2z+1=0

Wy multiply elements

14z^2+20z-50z+1=0

We add all the numbers together, and all the variables

14z^2-30z+1=0

a = 14; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·14·1
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{211}}{2*14}=\frac{30-2\sqrt{211}}{28}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{211}}{2*14}=\frac{30+2\sqrt{211}}{28}
$