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(3x+5)(7x-15)=x
We move all terms to the left:
(3x+5)(7x-15)-(x)=0
We add all the numbers together, and all the variables
-1x+(3x+5)(7x-15)=0
We multiply parentheses ..
(+21x^2-45x+35x-75)-1x=0
We get rid of parentheses
21x^2-45x+35x-1x-75=0
We add all the numbers together, and all the variables
21x^2-11x-75=0
a = 21; b = -11; c = -75;
Δ = b2-4ac
Δ = -112-4·21·(-75)
Δ = 6421
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{6421}}{2*21}=\frac{11-\sqrt{6421}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{6421}}{2*21}=\frac{11+\sqrt{6421}}{42} $
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