X=3/4y-45

Solution for X=3/4y-45 equation:

X=3/4X-45

We move all terms to the left:

X-(3/4X-45)=0


Domain of the equation: 4X-45)!=0

X∈R


We get rid of parentheses

X-3/4X+45=0

We multiply all the terms by the denominator


X*4X+45*4X-3=0

Wy multiply elements

4X^2+180X-3=0

a = 4; b = 180; c = -3;
Δ = b2-4ac
Δ = 1802-4·4·(-3)
Δ = 32448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32448}=\sqrt{10816*3}=\sqrt{10816}*\sqrt{3}=104\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-104\sqrt{3}}{2*4}=\frac{-180-104\sqrt{3}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+104\sqrt{3}}{2*4}=\frac{-180+104\sqrt{3}}{8}
$