3x^2-22x+7=-4x-17

Solution for 3x^2-22x+7=-4x-17 equation:

3x^2-22x+7=-4x-17

We move all terms to the left:

3x^2-22x+7-(-4x-17)=0

We get rid of parentheses

3x^2-22x+4x+17+7=0

We add all the numbers together, and all the variables

3x^2-18x+24=0

a = 3; b = -18; c = +24;
Δ = b2-4ac
Δ = -182-4·3·24
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*3}=\frac{12}{6}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*3}=\frac{24}{6}
=4
$