(1/4)(4x+7)=5

Solution for (1/4)(4x+7)=5 equation:

(1/4)(4x+7)=5

We move all terms to the left:

(1/4)(4x+7)-(5)=0


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

x∈R


We add all the numbers together, and all the variables

(+1/4)(4x+7)-5=0

We multiply parentheses ..

(+4x^2+1/4*7)-5=0

We multiply all the terms by the denominator


(+4x^2+1-5*4*7)=0

We get rid of parentheses

4x^2+1-5*4*7=0

We add all the numbers together, and all the variables

4x^2-139=0

a = 4; b = 0; c = -139;
Δ = b2-4ac
Δ = 02-4·4·(-139)
Δ = 2224
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:

$\sqrt{\Delta}=\sqrt{2224}=\sqrt{16*139}=\sqrt{16}*\sqrt{139}=4\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{139}}{2*4}=\frac{0-4\sqrt{139}}{8}
=-\frac{4\sqrt{139}}{8}
=-\frac{\sqrt{139}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{139}}{2*4}=\frac{0+4\sqrt{139}}{8}
=\frac{4\sqrt{139}}{8}
=\frac{\sqrt{139}}{2}
$