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(1x-8)(7x+4)=x-7
We move all terms to the left:
(1x-8)(7x+4)-(x-7)=0
We add all the numbers together, and all the variables
(x-8)(7x+4)-(x-7)=0
We get rid of parentheses
(x-8)(7x+4)-x+7=0
We multiply parentheses ..
(+7x^2+4x-56x-32)-x+7=0
We add all the numbers together, and all the variables
(+7x^2+4x-56x-32)-1x+7=0
We get rid of parentheses
7x^2+4x-56x-1x-32+7=0
We add all the numbers together, and all the variables
7x^2-53x-25=0
a = 7; b = -53; c = -25;
Δ = b2-4ac
Δ = -532-4·7·(-25)
Δ = 3509
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3509}=\sqrt{121*29}=\sqrt{121}*\sqrt{29}=11\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-11\sqrt{29}}{2*7}=\frac{53-11\sqrt{29}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+11\sqrt{29}}{2*7}=\frac{53+11\sqrt{29}}{14} $
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