X=-3/4y+5

Solution for X=-3/4y+5 equation:

X=-3/4X+5

We move all terms to the left:

X-(-3/4X+5)=0


Domain of the equation: 4X+5)!=0

X∈R


We get rid of parentheses

X+3/4X-5=0

We multiply all the terms by the denominator


X*4X-5*4X+3=0

Wy multiply elements

4X^2-20X+3=0

a = 4; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·4·3
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{22}}{2*4}=\frac{20-4\sqrt{22}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{22}}{2*4}=\frac{20+4\sqrt{22}}{8}
$