(3/2)(5x+7)=16

Solution for (3/2)(5x+7)=16 equation:

(3/2)(5x+7)=16

We move all terms to the left:

(3/2)(5x+7)-(16)=0


Domain of the equation: 2)(5x+7)!=0

x∈R


We add all the numbers together, and all the variables

(+3/2)(5x+7)-16=0

We multiply parentheses ..

(+15x^2+3/2*7)-16=0

We multiply all the terms by the denominator


(+15x^2+3-16*2*7)=0

We get rid of parentheses

15x^2+3-16*2*7=0

We add all the numbers together, and all the variables

15x^2-221=0

a = 15; b = 0; c = -221;
Δ = b2-4ac
Δ = 02-4·15·(-221)
Δ = 13260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13260}=\sqrt{4*3315}=\sqrt{4}*\sqrt{3315}=2\sqrt{3315}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3315}}{2*15}=\frac{0-2\sqrt{3315}}{30}
=-\frac{2\sqrt{3315}}{30}
=-\frac{\sqrt{3315}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3315}}{2*15}=\frac{0+2\sqrt{3315}}{30}
=\frac{2\sqrt{3315}}{30}
=\frac{\sqrt{3315}}{15}
$