3/4y+y=175

Solution for 3/4y+y=175 equation:

3/4y+y=175

We move all terms to the left:

3/4y+y-(175)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

y+3/4y-175=0

We multiply all the terms by the denominator


y*4y-175*4y+3=0

Wy multiply elements

4y^2-700y+3=0

a = 4; b = -700; c = +3;
Δ = b2-4ac
Δ = -7002-4·4·3
Δ = 489952
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:

$\sqrt{\Delta}=\sqrt{489952}=\sqrt{16*30622}=\sqrt{16}*\sqrt{30622}=4\sqrt{30622}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-4\sqrt{30622}}{2*4}=\frac{700-4\sqrt{30622}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+4\sqrt{30622}}{2*4}=\frac{700+4\sqrt{30622}}{8}
$