3(x+1)-5(x-2)2=x2

Solution for 3(x+1)-5(x-2)2=x2 equation:

3(x+1)-5(x-2)2=x2

We move all terms to the left:

3(x+1)-5(x-2)2-(x2)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-1x^2+3x-10x+3+20=0

We add all the numbers together, and all the variables

-1x^2-7x+23=0

a = -1; b = -7; c = +23;
Δ = b2-4ac
Δ = -72-4·(-1)·23
Δ = 141
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{-(-7)-\sqrt{141}}{2*-1}=\frac{7-\sqrt{141}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{141}}{2*-1}=\frac{7+\sqrt{141}}{-2}
$