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(6x-11)(4x-25)=124
We move all terms to the left:
(6x-11)(4x-25)-(124)=0
We multiply parentheses ..
(+24x^2-150x-44x+275)-124=0
We get rid of parentheses
24x^2-150x-44x+275-124=0
We add all the numbers together, and all the variables
24x^2-194x+151=0
a = 24; b = -194; c = +151;
Δ = b2-4ac
Δ = -1942-4·24·151
Δ = 23140
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23140}=\sqrt{4*5785}=\sqrt{4}*\sqrt{5785}=2\sqrt{5785}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-194)-2\sqrt{5785}}{2*24}=\frac{194-2\sqrt{5785}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-194)+2\sqrt{5785}}{2*24}=\frac{194+2\sqrt{5785}}{48} $
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