Y=5x+3/3x+7

Solution for Y=5x+3/3x+7 equation:

=5Y+3/3Y+7

We move all terms to the left:

-(5Y+3/3Y+7)=0


Domain of the equation: 3Y+7)!=0

Y∈R


We get rid of parentheses

-5Y-3/3Y-7=0

We multiply all the terms by the denominator


-5Y*3Y-7*3Y-3=0

Wy multiply elements

-15Y^2-21Y-3=0

a = -15; b = -21; c = -3;
Δ = b2-4ac
Δ = -212-4·(-15)·(-3)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{29}}{2*-15}=\frac{21-3\sqrt{29}}{-30}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{29}}{2*-15}=\frac{21+3\sqrt{29}}{-30}
$