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(3x-38)(7x-95)=47
We move all terms to the left:
(3x-38)(7x-95)-(47)=0
We multiply parentheses ..
(+21x^2-285x-266x+3610)-47=0
We get rid of parentheses
21x^2-285x-266x+3610-47=0
We add all the numbers together, and all the variables
21x^2-551x+3563=0
a = 21; b = -551; c = +3563;
Δ = b2-4ac
Δ = -5512-4·21·3563
Δ = 4309
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{-(-551)-\sqrt{4309}}{2*21}=\frac{551-\sqrt{4309}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-551)+\sqrt{4309}}{2*21}=\frac{551+\sqrt{4309}}{42} $
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