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(-7x+41)(-8x+19)=90
We move all terms to the left:
(-7x+41)(-8x+19)-(90)=0
We multiply parentheses ..
(+56x^2-133x-328x+779)-90=0
We get rid of parentheses
56x^2-133x-328x+779-90=0
We add all the numbers together, and all the variables
56x^2-461x+689=0
a = 56; b = -461; c = +689;
Δ = b2-4ac
Δ = -4612-4·56·689
Δ = 58185
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{58185}=\sqrt{9*6465}=\sqrt{9}*\sqrt{6465}=3\sqrt{6465}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-461)-3\sqrt{6465}}{2*56}=\frac{461-3\sqrt{6465}}{112} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-461)+3\sqrt{6465}}{2*56}=\frac{461+3\sqrt{6465}}{112} $
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