3x2+5x-1=x2-2x-7

Solution for 3x2+5x-1=x2-2x-7 equation:

3x^2+5x-1=x2-2x-7

We move all terms to the left:

3x^2+5x-1-(x2-2x-7)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+7x+6=0

a = 2; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·2·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*2}=\frac{-6}{4}
=-1+1/2
$