3x^2+12x-23=17-7x

Solution for 3x^2+12x-23=17-7x equation:

3x^2+12x-23=17-7x

We move all terms to the left:

3x^2+12x-23-(17-7x)=0

We add all the numbers together, and all the variables

3x^2+12x-(-7x+17)-23=0

We get rid of parentheses

3x^2+12x+7x-17-23=0

We add all the numbers together, and all the variables

3x^2+19x-40=0

a = 3; b = 19; c = -40;
Δ = b2-4ac
Δ = 192-4·3·(-40)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-29}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+29}{2*3}=\frac{10}{6}
=1+2/3
$