Y-5=(3/4)(x+3)

Solution for Y-5=(3/4)(x+3) equation:

-5=(3/4)(Y+3)

We move all terms to the left:

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


Domain of the equation: 4)(Y+3))!=0

Y∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+3Y^2+3/4*3))-5=0

We multiply all the terms by the denominator


-((+3Y^2+3-5*4*3))=0


We calculate terms in parentheses: -((+3Y^2+3-5*4*3)), so:

(+3Y^2+3-5*4*3)

We get rid of parentheses

3Y^2+3-5*4*3

We add all the numbers together, and all the variables

3Y^2-57

Back to the equation:

-(3Y^2-57)


We get rid of parentheses

-3Y^2+57=0

a = -3; b = 0; c = +57;
Δ = b2-4ac
Δ = 02-4·(-3)·57
Δ = 684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{19}}{2*-3}=\frac{0-6\sqrt{19}}{-6}
=-\frac{6\sqrt{19}}{-6}
=-\frac{\sqrt{19}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{19}}{2*-3}=\frac{0+6\sqrt{19}}{-6}
=\frac{6\sqrt{19}}{-6}
=\frac{\sqrt{19}}{-1}
$