1/4z=-6z+15

Solution for 1/4z=-6z+15 equation:

1/4z=-6z+15

We move all terms to the left:

1/4z-(-6z+15)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R


We get rid of parentheses

1/4z+6z-15=0

We multiply all the terms by the denominator


6z*4z-15*4z+1=0

Wy multiply elements

24z^2-60z+1=0

a = 24; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·24·1
Δ = 3504
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:

$\sqrt{\Delta}=\sqrt{3504}=\sqrt{16*219}=\sqrt{16}*\sqrt{219}=4\sqrt{219}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{219}}{2*24}=\frac{60-4\sqrt{219}}{48}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{219}}{2*24}=\frac{60+4\sqrt{219}}{48}
$