y=7/2X+5

Solution for y=7/2X+5 equation:

y=7/2y+5

We move all terms to the left:

y-(7/2y+5)=0


Domain of the equation: 2y+5)!=0

y∈R


We get rid of parentheses

y-7/2y-5=0

We multiply all the terms by the denominator


y*2y-5*2y-7=0

Wy multiply elements

2y^2-10y-7=0

a = 2; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·2·(-7)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{39}}{2*2}=\frac{10-2\sqrt{39}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*2}=\frac{10+2\sqrt{39}}{4}
$