X=3/4y-45

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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} $

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