2x(2x-10)-8=-2(14-3x)

Solution for 2x(2x-10)-8=-2(14-3x) equation:

2x(2x-10)-8=-2(14-3x)

We move all terms to the left:

2x(2x-10)-8-(-2(14-3x))=0

We add all the numbers together, and all the variables

2x(2x-10)-(-2(-3x+14))-8=0

We multiply parentheses

4x^2-20x-(-2(-3x+14))-8=0


We calculate terms in parentheses: -(-2(-3x+14)), so:

-2(-3x+14)

We multiply parentheses

6x-28

Back to the equation:

-(6x-28)


We get rid of parentheses

4x^2-20x-6x+28-8=0

We add all the numbers together, and all the variables

4x^2-26x+20=0

a = 4; b = -26; c = +20;
Δ = b2-4ac
Δ = -262-4·4·20
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{89}}{2*4}=\frac{26-2\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{89}}{2*4}=\frac{26+2\sqrt{89}}{8}
$