7x+4=2x(x-8)

Solution for 7x+4=2x(x-8) equation:

7x+4=2x(x-8)

We move all terms to the left:

7x+4-(2x(x-8))=0


We calculate terms in parentheses: -(2x(x-8)), so:

2x(x-8)

We multiply parentheses

2x^2-16x

Back to the equation:

-(2x^2-16x)


We get rid of parentheses

-2x^2+7x+16x+4=0

We add all the numbers together, and all the variables

-2x^2+23x+4=0

a = -2; b = 23; c = +4;
Δ = b2-4ac
Δ = 232-4·(-2)·4
Δ = 561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{561}}{2*-2}=\frac{-23-\sqrt{561}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{561}}{2*-2}=\frac{-23+\sqrt{561}}{-4}
$