4x2-78=5x2+19x

Solution for 4x2-78=5x2+19x equation:

4x^2-78=5x^2+19x

We move all terms to the left:

4x^2-78-(5x^2+19x)=0

We get rid of parentheses

4x^2-5x^2-19x-78=0

We add all the numbers together, and all the variables

-1x^2-19x-78=0

a = -1; b = -19; c = -78;
Δ = b2-4ac
Δ = -192-4·(-1)·(-78)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-7}{2*-1}=\frac{12}{-2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+7}{2*-1}=\frac{26}{-2}
=-13
$