14(4X+3)=7/2x=

Solution for 14(4X+3)=7/2x= equation:

14(4X+3)=7/2X=

We move all terms to the left:

14(4X+3)-(7/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

14(4X+3)-(+7/2X)=0

We multiply parentheses

56X-(+7/2X)+42=0

We get rid of parentheses

56X-7/2X+42=0

We multiply all the terms by the denominator


56X*2X+42*2X-7=0

Wy multiply elements

112X^2+84X-7=0

a = 112; b = 84; c = -7;
Δ = b2-4ac
Δ = 842-4·112·(-7)
Δ = 10192
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:

$\sqrt{\Delta}=\sqrt{10192}=\sqrt{784*13}=\sqrt{784}*\sqrt{13}=28\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-28\sqrt{13}}{2*112}=\frac{-84-28\sqrt{13}}{224}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+28\sqrt{13}}{2*112}=\frac{-84+28\sqrt{13}}{224}
$