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(5x-7)(7x-39)=90
We move all terms to the left:
(5x-7)(7x-39)-(90)=0
We multiply parentheses ..
(+35x^2-195x-49x+273)-90=0
We get rid of parentheses
35x^2-195x-49x+273-90=0
We add all the numbers together, and all the variables
35x^2-244x+183=0
a = 35; b = -244; c = +183;
Δ = b2-4ac
Δ = -2442-4·35·183
Δ = 33916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{33916}=\sqrt{4*8479}=\sqrt{4}*\sqrt{8479}=2\sqrt{8479}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-244)-2\sqrt{8479}}{2*35}=\frac{244-2\sqrt{8479}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-244)+2\sqrt{8479}}{2*35}=\frac{244+2\sqrt{8479}}{70} $
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