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(3x-11)(4x-7)+44=180
We move all terms to the left:
(3x-11)(4x-7)+44-(180)=0
We add all the numbers together, and all the variables
(3x-11)(4x-7)-136=0
We multiply parentheses ..
(+12x^2-21x-44x+77)-136=0
We get rid of parentheses
12x^2-21x-44x+77-136=0
We add all the numbers together, and all the variables
12x^2-65x-59=0
a = 12; b = -65; c = -59;
Δ = b2-4ac
Δ = -652-4·12·(-59)
Δ = 7057
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{7057}}{2*12}=\frac{65-\sqrt{7057}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{7057}}{2*12}=\frac{65+\sqrt{7057}}{24} $
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