-2x(x-5)-7=3x-4-7x

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

-2x(x-5)-7=3x-4-7x

We move all terms to the left:

-2x(x-5)-7-(3x-4-7x)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+14x-3=0

a = -2; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·(-2)·(-3)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{43}}{2*-2}=\frac{-14-2\sqrt{43}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{43}}{2*-2}=\frac{-14+2\sqrt{43}}{-4}
$