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(2x-11)(6x-7)=180
We move all terms to the left:
(2x-11)(6x-7)-(180)=0
We multiply parentheses ..
(+12x^2-14x-66x+77)-180=0
We get rid of parentheses
12x^2-14x-66x+77-180=0
We add all the numbers together, and all the variables
12x^2-80x-103=0
a = 12; b = -80; c = -103;
Δ = b2-4ac
Δ = -802-4·12·(-103)
Δ = 11344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11344}=\sqrt{16*709}=\sqrt{16}*\sqrt{709}=4\sqrt{709}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{709}}{2*12}=\frac{80-4\sqrt{709}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{709}}{2*12}=\frac{80+4\sqrt{709}}{24} $
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