(3x-7)(8x+2x)=(4x+4)(5-6)

Solution for (3x-7)(8x+2x)=(4x+4)(5-6) equation:

(3x-7)(8x+2x)=(4x+4)(5-6)

We move all terms to the left:

(3x-7)(8x+2x)-((4x+4)(5-6))=0

We add all the numbers together, and all the variables

(3x-7)(+10x)-((4x+4)(-1))=0

We multiply parentheses ..

(+30x^2-70x)-((4x+4)(-1))=0


We calculate terms in parentheses: -((4x+4)(-1)), so:

(4x+4)(-1)

We multiply parentheses ..

(-4x-4)

We get rid of parentheses

-4x-4

Back to the equation:

-(-4x-4)


We get rid of parentheses

30x^2-70x+4x+4=0

We add all the numbers together, and all the variables

30x^2-66x+4=0

a = 30; b = -66; c = +4;
Δ = b2-4ac
Δ = -662-4·30·4
Δ = 3876
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:

$\sqrt{\Delta}=\sqrt{3876}=\sqrt{4*969}=\sqrt{4}*\sqrt{969}=2\sqrt{969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{969}}{2*30}=\frac{66-2\sqrt{969}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{969}}{2*30}=\frac{66+2\sqrt{969}}{60}
$