8x+7=3x(x-2)

Solution for 8x+7=3x(x-2) equation:

8x+7=3x(x-2)

We move all terms to the left:

8x+7-(3x(x-2))=0


We calculate terms in parentheses: -(3x(x-2)), so:

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

-3x^2+8x+6x+7=0

We add all the numbers together, and all the variables

-3x^2+14x+7=0

a = -3; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-3)·7
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{70}}{2*-3}=\frac{-14-2\sqrt{70}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{70}}{2*-3}=\frac{-14+2\sqrt{70}}{-6}
$