12+2x(2x-3)=3x(x+5)-1

Solution for 12+2x(2x-3)=3x(x+5)-1 equation:

12+2x(2x-3)=3x(x+5)-1

We move all terms to the left:

12+2x(2x-3)-(3x(x+5)-1)=0

We multiply parentheses

4x^2-6x-(3x(x+5)-1)+12=0


We calculate terms in parentheses: -(3x(x+5)-1), so:

3x(x+5)-1

We multiply parentheses

3x^2+15x-1

Back to the equation:

-(3x^2+15x-1)


We get rid of parentheses

4x^2-3x^2-6x-15x+1+12=0

We add all the numbers together, and all the variables

x^2-21x+13=0

a = 1; b = -21; c = +13;
Δ = b2-4ac
Δ = -212-4·1·13
Δ = 389
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{-(-21)-\sqrt{389}}{2*1}=\frac{21-\sqrt{389}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{389}}{2*1}=\frac{21+\sqrt{389}}{2}
$