3x^2+10x+24=2x^2+29x+14

Solution for 3x^2+10x+24=2x^2+29x+14 equation:

3x^2+10x+24=2x^2+29x+14

We move all terms to the left:

3x^2+10x+24-(2x^2+29x+14)=0

We get rid of parentheses

3x^2-2x^2+10x-29x-14+24=0

We add all the numbers together, and all the variables

x^2-19x+10=0

a = 1; b = -19; c = +10;
Δ = b2-4ac
Δ = -192-4·1·10
Δ = 321
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{321}}{2*1}=\frac{19-\sqrt{321}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{321}}{2*1}=\frac{19+\sqrt{321}}{2}
$