2.25-3z=0.37z-3/4z

Solution for 2.25-3z=0.37z-3/4z equation:

2.25-3z=0.37z-3/4z

We move all terms to the left:

2.25-3z-(0.37z-3/4z)=0


Domain of the equation: 4z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

-3z-(+0.37z-3/4z)+2.25=0

We get rid of parentheses

-3z-0.37z+3/4z+2.25=0

We multiply all the terms by the denominator


-3z*4z-(0.37z)*4z+(2.25)*4z+3=0

We add all the numbers together, and all the variables

-3z*4z-(+0.37z)*4z+(2.25)*4z+3=0

We multiply parentheses

-0z^2-3z*4z+9z+3=0

Wy multiply elements

-0z^2-12z^2+9z+3=0

We add all the numbers together, and all the variables

-13z^2+9z+3=0

a = -13; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-13)·3
Δ = 237
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{237}}{2*-13}=\frac{-9-\sqrt{237}}{-26}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{237}}{2*-13}=\frac{-9+\sqrt{237}}{-26}
$