(6+2x)(4x)/2=60

Solution for (6+2x)(4x)/2=60 equation:

(6+2x)(4x)/2=60

We move all terms to the left:

(6+2x)(4x)/2-(60)=0

We add all the numbers together, and all the variables

(2x+6)4x/2-60=0

We multiply all the terms by the denominator


(2x+6)4x-60*2=0

We add all the numbers together, and all the variables

(2x+6)4x-120=0

We multiply parentheses

8x^2+24x-120=0

a = 8; b = 24; c = -120;
Δ = b2-4ac
Δ = 242-4·8·(-120)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{69}}{2*8}=\frac{-24-8\sqrt{69}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{69}}{2*8}=\frac{-24+8\sqrt{69}}{16}
$