(6x-47)(x+4)=90

Solution for (6x-47)(x+4)=90 equation:

(6x-47)(x+4)=90

We move all terms to the left:

(6x-47)(x+4)-(90)=0

We multiply parentheses ..

(+6x^2+24x-47x-188)-90=0

We get rid of parentheses

6x^2+24x-47x-188-90=0

We add all the numbers together, and all the variables

6x^2-23x-278=0

a = 6; b = -23; c = -278;
Δ = b2-4ac
Δ = -232-4·6·(-278)
Δ = 7201
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{-(-23)-\sqrt{7201}}{2*6}=\frac{23-\sqrt{7201}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{7201}}{2*6}=\frac{23+\sqrt{7201}}{12}
$