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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

7x+3x(x-3)-(-1x+5)+3=0

We multiply parentheses

3x^2+7x-9x-(-1x+5)+3=0

We get rid of parentheses

3x^2+7x-9x+1x-5+3=0

We add all the numbers together, and all the variables

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