(4/6)*(4x+3)=15

Solution for (4/6)*(4x+3)=15 equation:

(4/6)(4x+3)=15

We move all terms to the left:

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


Domain of the equation: 6)(4x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+16x^2+4/6*3)-15=0

We multiply all the terms by the denominator


(+16x^2+4-15*6*3)=0

We get rid of parentheses

16x^2+4-15*6*3=0

We add all the numbers together, and all the variables

16x^2-266=0

a = 16; b = 0; c = -266;
Δ = b2-4ac
Δ = 02-4·16·(-266)
Δ = 17024
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:

$\sqrt{\Delta}=\sqrt{17024}=\sqrt{64*266}=\sqrt{64}*\sqrt{266}=8\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{266}}{2*16}=\frac{0-8\sqrt{266}}{32}
=-\frac{8\sqrt{266}}{32}
=-\frac{\sqrt{266}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{266}}{2*16}=\frac{0+8\sqrt{266}}{32}
=\frac{8\sqrt{266}}{32}
=\frac{\sqrt{266}}{4}
$