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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

4x-(-2x(-2x+5))+7=0


We calculate terms in parentheses: -(-2x(-2x+5)), so:

-2x(-2x+5)

We multiply parentheses

4x^2-10x

Back to the equation:

-(4x^2-10x)


We get rid of parentheses

-4x^2+4x+10x+7=0

We add all the numbers together, and all the variables

-4x^2+14x+7=0

a = -4; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-4)·7
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{77}}{2*-4}=\frac{-14-2\sqrt{77}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{77}}{2*-4}=\frac{-14+2\sqrt{77}}{-8}
$