7.5y-4=3/4y-7

Solution for 7.5y-4=3/4y-7 equation:

7.5y-4=3/4y-7

We move all terms to the left:

7.5y-4-(3/4y-7)=0


Domain of the equation: 4y-7)!=0

y∈R


We get rid of parentheses

7.5y-3/4y+7-4=0

We multiply all the terms by the denominator


(7.5y)*4y+7*4y-4*4y-3=0

We add all the numbers together, and all the variables

(+7.5y)*4y+7*4y-4*4y-3=0

We multiply parentheses

28y^2+7*4y-4*4y-3=0

Wy multiply elements

28y^2+28y-16y-3=0

We add all the numbers together, and all the variables

28y^2+12y-3=0

a = 28; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·28·(-3)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{30}}{2*28}=\frac{-12-4\sqrt{30}}{56}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{30}}{2*28}=\frac{-12+4\sqrt{30}}{56}
$