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(12x-1)(9x-15)=53
We move all terms to the left:
(12x-1)(9x-15)-(53)=0
We multiply parentheses ..
(+108x^2-180x-9x+15)-53=0
We get rid of parentheses
108x^2-180x-9x+15-53=0
We add all the numbers together, and all the variables
108x^2-189x-38=0
a = 108; b = -189; c = -38;
Δ = b2-4ac
Δ = -1892-4·108·(-38)
Δ = 52137
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52137}=\sqrt{9*5793}=\sqrt{9}*\sqrt{5793}=3\sqrt{5793}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-3\sqrt{5793}}{2*108}=\frac{189-3\sqrt{5793}}{216} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+3\sqrt{5793}}{2*108}=\frac{189+3\sqrt{5793}}{216} $
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