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(5x-23)(7x-1)=180
We move all terms to the left:
(5x-23)(7x-1)-(180)=0
We multiply parentheses ..
(+35x^2-5x-161x+23)-180=0
We get rid of parentheses
35x^2-5x-161x+23-180=0
We add all the numbers together, and all the variables
35x^2-166x-157=0
a = 35; b = -166; c = -157;
Δ = b2-4ac
Δ = -1662-4·35·(-157)
Δ = 49536
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{49536}=\sqrt{576*86}=\sqrt{576}*\sqrt{86}=24\sqrt{86}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-24\sqrt{86}}{2*35}=\frac{166-24\sqrt{86}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+24\sqrt{86}}{2*35}=\frac{166+24\sqrt{86}}{70} $
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