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(6x-7)(4x-1)=90
We move all terms to the left:
(6x-7)(4x-1)-(90)=0
We multiply parentheses ..
(+24x^2-6x-28x+7)-90=0
We get rid of parentheses
24x^2-6x-28x+7-90=0
We add all the numbers together, and all the variables
24x^2-34x-83=0
a = 24; b = -34; c = -83;
Δ = b2-4ac
Δ = -342-4·24·(-83)
Δ = 9124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9124}=\sqrt{4*2281}=\sqrt{4}*\sqrt{2281}=2\sqrt{2281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{2281}}{2*24}=\frac{34-2\sqrt{2281}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{2281}}{2*24}=\frac{34+2\sqrt{2281}}{48} $
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