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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(5x+3x(x-2)+5), so:

5x+3x(x-2)+5

We multiply parentheses

3x^2+5x-6x+5

We add all the numbers together, and all the variables

3x^2-1x+5

Back to the equation:

-(3x^2-1x+5)


We get rid of parentheses

-3x^2+1x-5+7=0

We add all the numbers together, and all the variables

-3x^2+x+2=0

a = -3; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-3)·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-3}=\frac{4}{-6}
=-2/3
$