5x(2-x)+7-10x=6

Solution for 5x(2-x)+7-10x=6 equation:

5x(2-x)+7-10x=6

We move all terms to the left:

5x(2-x)+7-10x-(6)=0

We add all the numbers together, and all the variables

5x(-1x+2)-10x+7-6=0

We add all the numbers together, and all the variables

-10x+5x(-1x+2)+1=0

We multiply parentheses

-5x^2-10x+10x+1=0

We add all the numbers together, and all the variables

-5x^2+1=0

a = -5; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-5)·1
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*-5}=\frac{0-2\sqrt{5}}{-10}
=-\frac{2\sqrt{5}}{-10}
=-\frac{\sqrt{5}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*-5}=\frac{0+2\sqrt{5}}{-10}
=\frac{2\sqrt{5}}{-10}
=\frac{\sqrt{5}}{-5}
$