10-5x(x-2)=3+4x

Solution for 10-5x(x-2)=3+4x equation:

10-5x(x-2)=3+4x

We move all terms to the left:

10-5x(x-2)-(3+4x)=0

We add all the numbers together, and all the variables

-5x(x-2)-(4x+3)+10=0

We multiply parentheses

-5x^2+10x-(4x+3)+10=0

We get rid of parentheses

-5x^2+10x-4x-3+10=0

We add all the numbers together, and all the variables

-5x^2+6x+7=0

a = -5; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-5)·7
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{11}}{2*-5}=\frac{-6-4\sqrt{11}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{11}}{2*-5}=\frac{-6+4\sqrt{11}}{-10}
$