3x^2+7x-15=x-3

Solution for 3x^2+7x-15=x-3 equation:

3x^2+7x-15=x-3

We move all terms to the left:

3x^2+7x-15-(x-3)=0

We get rid of parentheses

3x^2+7x-x+3-15=0

We add all the numbers together, and all the variables

3x^2+6x-12=0

a = 3; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·3·(-12)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*3}=\frac{-6-6\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*3}=\frac{-6+6\sqrt{5}}{6}
$