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(7+13x)(-20+16x)=x
We move all terms to the left:
(7+13x)(-20+16x)-(x)=0
We add all the numbers together, and all the variables
(13x+7)(16x-20)-x=0
We add all the numbers together, and all the variables
-1x+(13x+7)(16x-20)=0
We multiply parentheses ..
(+208x^2-260x+112x-140)-1x=0
We get rid of parentheses
208x^2-260x+112x-1x-140=0
We add all the numbers together, and all the variables
208x^2-149x-140=0
a = 208; b = -149; c = -140;
Δ = b2-4ac
Δ = -1492-4·208·(-140)
Δ = 138681
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{138681}=\sqrt{9*15409}=\sqrt{9}*\sqrt{15409}=3\sqrt{15409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-149)-3\sqrt{15409}}{2*208}=\frac{149-3\sqrt{15409}}{416} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-149)+3\sqrt{15409}}{2*208}=\frac{149+3\sqrt{15409}}{416} $
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