(6x-7)(4x+23)=90

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Solution for (6x-7)(4x+23)=90 equation:



(6x-7)(4x+23)=90
We move all terms to the left:
(6x-7)(4x+23)-(90)=0
We multiply parentheses ..
(+24x^2+138x-28x-161)-90=0
We get rid of parentheses
24x^2+138x-28x-161-90=0
We add all the numbers together, and all the variables
24x^2+110x-251=0
a = 24; b = 110; c = -251;
Δ = b2-4ac
Δ = 1102-4·24·(-251)
Δ = 36196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{36196}=\sqrt{4*9049}=\sqrt{4}*\sqrt{9049}=2\sqrt{9049}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{9049}}{2*24}=\frac{-110-2\sqrt{9049}}{48} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{9049}}{2*24}=\frac{-110+2\sqrt{9049}}{48} $

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