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(5x+9)(7x-9)=90
We move all terms to the left:
(5x+9)(7x-9)-(90)=0
We multiply parentheses ..
(+35x^2-45x+63x-81)-90=0
We get rid of parentheses
35x^2-45x+63x-81-90=0
We add all the numbers together, and all the variables
35x^2+18x-171=0
a = 35; b = 18; c = -171;
Δ = b2-4ac
Δ = 182-4·35·(-171)
Δ = 24264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24264}=\sqrt{36*674}=\sqrt{36}*\sqrt{674}=6\sqrt{674}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{674}}{2*35}=\frac{-18-6\sqrt{674}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{674}}{2*35}=\frac{-18+6\sqrt{674}}{70} $
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