(1/4)(3x+7)=4

Solution for (1/4)(3x+7)=4 equation:

(1/4)(3x+7)=4

We move all terms to the left:

(1/4)(3x+7)-(4)=0


Domain of the equation: 4)(3x+7)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(3x+7)-4=0

We multiply parentheses ..

(+3x^2+1/4*7)-4=0

We multiply all the terms by the denominator


(+3x^2+1-4*4*7)=0

We get rid of parentheses

3x^2+1-4*4*7=0

We add all the numbers together, and all the variables

3x^2-111=0

a = 3; b = 0; c = -111;
Δ = b2-4ac
Δ = 02-4·3·(-111)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{37}}{2*3}=\frac{0-6\sqrt{37}}{6}
=-\frac{6\sqrt{37}}{6}
=-\sqrt{37}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{37}}{2*3}=\frac{0+6\sqrt{37}}{6}
=\frac{6\sqrt{37}}{6}
=\sqrt{37}
$