5+(4/7)(21+3x)=41

Solution for 5+(4/7)(21+3x)=41 equation:

5+(4/7)(21+3x)=41

We move all terms to the left:

5+(4/7)(21+3x)-(41)=0


Domain of the equation: 7)(21+3x)!=0

x∈R


We add all the numbers together, and all the variables

(+4/7)(3x+21)+5-41=0

We add all the numbers together, and all the variables

(+4/7)(3x+21)-36=0

We multiply parentheses ..

(+12x^2+4/7*21)-36=0

We multiply all the terms by the denominator


(+12x^2+4-36*7*21)=0

We get rid of parentheses

12x^2+4-36*7*21=0

We add all the numbers together, and all the variables

12x^2-5288=0

a = 12; b = 0; c = -5288;
Δ = b2-4ac
Δ = 02-4·12·(-5288)
Δ = 253824
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:

$\sqrt{\Delta}=\sqrt{253824}=\sqrt{64*3966}=\sqrt{64}*\sqrt{3966}=8\sqrt{3966}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3966}}{2*12}=\frac{0-8\sqrt{3966}}{24}
=-\frac{8\sqrt{3966}}{24}
=-\frac{\sqrt{3966}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3966}}{2*12}=\frac{0+8\sqrt{3966}}{24}
=\frac{8\sqrt{3966}}{24}
=\frac{\sqrt{3966}}{3}
$