3x^2-29x=-2x^2-3x-24

Solution for 3x^2-29x=-2x^2-3x-24 equation:

3x^2-29x=-2x^2-3x-24

We move all terms to the left:

3x^2-29x-(-2x^2-3x-24)=0

We get rid of parentheses

3x^2+2x^2+3x-29x+24=0

We add all the numbers together, and all the variables

5x^2-26x+24=0

a = 5; b = -26; c = +24;
Δ = b2-4ac
Δ = -262-4·5·24
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-14}{2*5}=\frac{12}{10}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+14}{2*5}=\frac{40}{10}
=4
$