6x+4=(1/2)(4x+56)

Solution for 6x+4=(1/2)(4x+56) equation:

6x+4=(1/2)(4x+56)

We move all terms to the left:

6x+4-((1/2)(4x+56))=0


Domain of the equation: 2)(4x+56))!=0

x∈R


We add all the numbers together, and all the variables

6x-((+1/2)(4x+56))+4=0

We multiply parentheses ..

-((+4x^2+1/2*56))+6x+4=0

We multiply all the terms by the denominator


-((+4x^2+1+6x*2*56))+4*2*56))=0


We calculate terms in parentheses: -((+4x^2+1+6x*2*56)), so:

(+4x^2+1+6x*2*56)

We get rid of parentheses

4x^2+6x*2*56+1

Wy multiply elements

4x^2+672x*5+1

Wy multiply elements

4x^2+3360x+1

Back to the equation:

-(4x^2+3360x+1)


We add all the numbers together, and all the variables

-(4x^2+3360x+1)=0

We get rid of parentheses

-4x^2-3360x-1=0

a = -4; b = -3360; c = -1;
Δ = b2-4ac
Δ = -33602-4·(-4)·(-1)
Δ = 11289584
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:

$\sqrt{\Delta}=\sqrt{11289584}=\sqrt{13456*839}=\sqrt{13456}*\sqrt{839}=116\sqrt{839}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3360)-116\sqrt{839}}{2*-4}=\frac{3360-116\sqrt{839}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3360)+116\sqrt{839}}{2*-4}=\frac{3360+116\sqrt{839}}{-8}
$