10x(1/2x+6)=8

Solution for 10x(1/2x+6)=8 equation:

10x(1/2x+6)=8

We move all terms to the left:

10x(1/2x+6)-(8)=0


Domain of the equation: 2x+6)!=0

x∈R


We multiply parentheses

10x^2+60x-8=0

a = 10; b = 60; c = -8;
Δ = b2-4ac
Δ = 602-4·10·(-8)
Δ = 3920
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:

$\sqrt{\Delta}=\sqrt{3920}=\sqrt{784*5}=\sqrt{784}*\sqrt{5}=28\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-28\sqrt{5}}{2*10}=\frac{-60-28\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+28\sqrt{5}}{2*10}=\frac{-60+28\sqrt{5}}{20}
$