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(8x-4)(3x+17)+(17x-23)=180
We move all terms to the left:
(8x-4)(3x+17)+(17x-23)-(180)=0
We get rid of parentheses
(8x-4)(3x+17)+17x-23-180=0
We multiply parentheses ..
(+24x^2+136x-12x-68)+17x-23-180=0
We add all the numbers together, and all the variables
(+24x^2+136x-12x-68)+17x-203=0
We get rid of parentheses
24x^2+136x-12x+17x-68-203=0
We add all the numbers together, and all the variables
24x^2+141x-271=0
a = 24; b = 141; c = -271;
Δ = b2-4ac
Δ = 1412-4·24·(-271)
Δ = 45897
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{-(141)-\sqrt{45897}}{2*24}=\frac{-141-\sqrt{45897}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(141)+\sqrt{45897}}{2*24}=\frac{-141+\sqrt{45897}}{48} $
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