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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(2(x-4)x), so:

2(x-4)x

We multiply parentheses

2x^2-8x

Back to the equation:

-(2x^2-8x)


We get rid of parentheses

-2x^2-3x+8x+10=0

We add all the numbers together, and all the variables

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

a = -2; b = 5; c = +10;
Δ = b2-4ac
Δ = 52-4·(-2)·10
Δ = 105
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{-(5)-\sqrt{105}}{2*-2}=\frac{-5-\sqrt{105}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{105}}{2*-2}=\frac{-5+\sqrt{105}}{-4}
$