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 = 32352
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:

$\sqrt{\Delta}=\sqrt{32352}=\sqrt{16*2022}=\sqrt{16}*\sqrt{2022}=4\sqrt{2022}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-4\sqrt{2022}}{2*4}=\frac{180-4\sqrt{2022}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+4\sqrt{2022}}{2*4}=\frac{180+4\sqrt{2022}}{8}
$