5-0.5(4x+6)=2x(x-7)

Solution for 5-0.5(4x+6)=2x(x-7) equation:

5-0.5(4x+6)=2x(x-7)

We move all terms to the left:

5-0.5(4x+6)-(2x(x-7))=0

We multiply parentheses

-2x-(2x(x-7))-3+5=0


We calculate terms in parentheses: -(2x(x-7)), so:

2x(x-7)

We multiply parentheses

2x^2-14x

Back to the equation:

-(2x^2-14x)


We add all the numbers together, and all the variables

-2x-(2x^2-14x)+2=0

We get rid of parentheses

-2x^2-2x+14x+2=0

We add all the numbers together, and all the variables

-2x^2+12x+2=0

a = -2; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-2)·2
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*-2}=\frac{-12-4\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*-2}=\frac{-12+4\sqrt{10}}{-4}
$