(4x-5)x-69=78

Solution for (4x-5)x-69=78 equation:

(4x-5)x-69=78

We move all terms to the left:

(4x-5)x-69-(78)=0

We add all the numbers together, and all the variables

(4x-5)x-147=0

We multiply parentheses

4x^2-5x-147=0

a = 4; b = -5; c = -147;
Δ = b2-4ac
Δ = -52-4·4·(-147)
Δ = 2377
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{-(-5)-\sqrt{2377}}{2*4}=\frac{5-\sqrt{2377}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2377}}{2*4}=\frac{5+\sqrt{2377}}{8}
$