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(10x+9)(6x-13)=360
We move all terms to the left:
(10x+9)(6x-13)-(360)=0
We multiply parentheses ..
(+60x^2-130x+54x-117)-360=0
We get rid of parentheses
60x^2-130x+54x-117-360=0
We add all the numbers together, and all the variables
60x^2-76x-477=0
a = 60; b = -76; c = -477;
Δ = b2-4ac
Δ = -762-4·60·(-477)
Δ = 120256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{120256}=\sqrt{64*1879}=\sqrt{64}*\sqrt{1879}=8\sqrt{1879}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-8\sqrt{1879}}{2*60}=\frac{76-8\sqrt{1879}}{120} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+8\sqrt{1879}}{2*60}=\frac{76+8\sqrt{1879}}{120} $
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