-4x(x-5)+8x=7(x-1)

Solution for -4x(x-5)+8x=7(x-1) equation:

-4x(x-5)+8x=7(x-1)

We move all terms to the left:

-4x(x-5)+8x-(7(x-1))=0

We add all the numbers together, and all the variables

8x-4x(x-5)-(7(x-1))=0

We multiply parentheses

-4x^2+8x+20x-(7(x-1))=0


We calculate terms in parentheses: -(7(x-1)), so:

7(x-1)

We multiply parentheses

7x-7

Back to the equation:

-(7x-7)


We add all the numbers together, and all the variables

-4x^2+28x-(7x-7)=0

We get rid of parentheses

-4x^2+28x-7x+7=0

We add all the numbers together, and all the variables

-4x^2+21x+7=0

a = -4; b = 21; c = +7;
Δ = b2-4ac
Δ = 212-4·(-4)·7
Δ = 553
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{553}}{2*-4}=\frac{-21-\sqrt{553}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{553}}{2*-4}=\frac{-21+\sqrt{553}}{-8}
$