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(9x-1)(6x+58)=87
We move all terms to the left:
(9x-1)(6x+58)-(87)=0
We multiply parentheses ..
(+54x^2+522x-6x-58)-87=0
We get rid of parentheses
54x^2+522x-6x-58-87=0
We add all the numbers together, and all the variables
54x^2+516x-145=0
a = 54; b = 516; c = -145;
Δ = b2-4ac
Δ = 5162-4·54·(-145)
Δ = 297576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{297576}=\sqrt{36*8266}=\sqrt{36}*\sqrt{8266}=6\sqrt{8266}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(516)-6\sqrt{8266}}{2*54}=\frac{-516-6\sqrt{8266}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(516)+6\sqrt{8266}}{2*54}=\frac{-516+6\sqrt{8266}}{108} $
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