1/2*10x+6=8x-6

Solution for 1/2*10x+6=8x-6 equation:

1/2*10x+6=8x-6

We move all terms to the left:

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


Domain of the equation: 2*10x!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/2*10x-8x+6+6=0

We multiply all the terms by the denominator


-8x*2*10x+6*2*10x+6*2*10x+1=0

Wy multiply elements

-160x^2*1+120x*1+120x*1+1=0

Wy multiply elements

-160x^2+120x+120x+1=0

We add all the numbers together, and all the variables

-160x^2+240x+1=0

a = -160; b = 240; c = +1;
Δ = b2-4ac
Δ = 2402-4·(-160)·1
Δ = 58240
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:

$\sqrt{\Delta}=\sqrt{58240}=\sqrt{64*910}=\sqrt{64}*\sqrt{910}=8\sqrt{910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-8\sqrt{910}}{2*-160}=\frac{-240-8\sqrt{910}}{-320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+8\sqrt{910}}{2*-160}=\frac{-240+8\sqrt{910}}{-320}
$