4x(7/2+x)=31

Solution for 4x(7/2+x)=31 equation:

4x(7/2+x)=31

We move all terms to the left:

4x(7/2+x)-(31)=0


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

We move all terms containing x to the left, all other terms to the right

x)!=-2

x!=-2/1

x!=-2

x∈R


We add all the numbers together, and all the variables

4x(+x+7/2)-31=0

We multiply parentheses

4x^2+28x^2-31=0

We add all the numbers together, and all the variables

32x^2-31=0

a = 32; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·32·(-31)
Δ = 3968
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:

$\sqrt{\Delta}=\sqrt{3968}=\sqrt{64*62}=\sqrt{64}*\sqrt{62}=8\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{62}}{2*32}=\frac{0-8\sqrt{62}}{64}
=-\frac{8\sqrt{62}}{64}
=-\frac{\sqrt{62}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{62}}{2*32}=\frac{0+8\sqrt{62}}{64}
=\frac{8\sqrt{62}}{64}
=\frac{\sqrt{62}}{8}
$