4x^2+7x-17=3x^2-12x-3

Solution for 4x^2+7x-17=3x^2-12x-3 equation:

4x^2+7x-17=3x^2-12x-3

We move all terms to the left:

4x^2+7x-17-(3x^2-12x-3)=0

We get rid of parentheses

4x^2-3x^2+7x+12x+3-17=0

We add all the numbers together, and all the variables

x^2+19x-14=0

a = 1; b = 19; c = -14;
Δ = b2-4ac
Δ = 192-4·1·(-14)
Δ = 417
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{-(19)-\sqrt{417}}{2*1}=\frac{-19-\sqrt{417}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{417}}{2*1}=\frac{-19+\sqrt{417}}{2}
$