(4/3)(15-6y)-7=-11

Solution for (4/3)(15-6y)-7=-11 equation:

(4/3)(15-6y)-7=-11

We move all terms to the left:

(4/3)(15-6y)-7-(-11)=0


Domain of the equation: 3)(15-6y)!=0

y∈R


We add all the numbers together, and all the variables

(+4/3)(-6y+15)-7-(-11)=0

We add all the numbers together, and all the variables

(+4/3)(-6y+15)+4=0

We multiply parentheses ..

(-24y^2+4/3*15)+4=0

We multiply all the terms by the denominator


(-24y^2+4+4*3*15)=0

We get rid of parentheses

-24y^2+4+4*3*15=0

We add all the numbers together, and all the variables

-24y^2+184=0

a = -24; b = 0; c = +184;
Δ = b2-4ac
Δ = 02-4·(-24)·184
Δ = 17664
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:

$\sqrt{\Delta}=\sqrt{17664}=\sqrt{256*69}=\sqrt{256}*\sqrt{69}=16\sqrt{69}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{69}}{2*-24}=\frac{0-16\sqrt{69}}{-48}
=-\frac{16\sqrt{69}}{-48}
=-\frac{\sqrt{69}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{69}}{2*-24}=\frac{0+16\sqrt{69}}{-48}
=\frac{16\sqrt{69}}{-48}
=\frac{\sqrt{69}}{-3}
$