4x-40=7x(-2x+2)

Solution for 4x-40=7x(-2x+2) equation:

4x-40=7x(-2x+2)

We move all terms to the left:

4x-40-(7x(-2x+2))=0


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

7x(-2x+2)

We multiply parentheses

-14x^2+14x

Back to the equation:

-(-14x^2+14x)


We get rid of parentheses

14x^2-14x+4x-40=0

We add all the numbers together, and all the variables

14x^2-10x-40=0

a = 14; b = -10; c = -40;
Δ = b2-4ac
Δ = -102-4·14·(-40)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{65}}{2*14}=\frac{10-6\sqrt{65}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{65}}{2*14}=\frac{10+6\sqrt{65}}{28}
$