6x^2+24x+35=5x^2+39x-19

Solution for 6x^2+24x+35=5x^2+39x-19 equation:

6x^2+24x+35=5x^2+39x-19

We move all terms to the left:

6x^2+24x+35-(5x^2+39x-19)=0

We get rid of parentheses

6x^2-5x^2+24x-39x+19+35=0

We add all the numbers together, and all the variables

x^2-15x+54=0

a = 1; b = -15; c = +54;
Δ = b2-4ac
Δ = -152-4·1·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*1}=\frac{18}{2}
=9
$