(x+3)(x-1)=-3x+4

Solution for (x+3)(x-1)=-3x+4 equation:

(x+3)(x-1)=-3x+4

We move all terms to the left:

(x+3)(x-1)-(-3x+4)=0

We get rid of parentheses

(x+3)(x-1)+3x-4=0

We multiply parentheses ..

(+x^2-1x+3x-3)+3x-4=0

We get rid of parentheses

x^2-1x+3x+3x-3-4=0

We add all the numbers together, and all the variables

x^2+5x-7=0

a = 1; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·1·(-7)
Δ = 53
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{53}}{2*1}=\frac{-5-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{53}}{2*1}=\frac{-5+\sqrt{53}}{2}
$