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(6x+7)(3x-16)=180
We move all terms to the left:
(6x+7)(3x-16)-(180)=0
We multiply parentheses ..
(+18x^2-96x+21x-112)-180=0
We get rid of parentheses
18x^2-96x+21x-112-180=0
We add all the numbers together, and all the variables
18x^2-75x-292=0
a = 18; b = -75; c = -292;
Δ = b2-4ac
Δ = -752-4·18·(-292)
Δ = 26649
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26649}=\sqrt{81*329}=\sqrt{81}*\sqrt{329}=9\sqrt{329}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-9\sqrt{329}}{2*18}=\frac{75-9\sqrt{329}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+9\sqrt{329}}{2*18}=\frac{75+9\sqrt{329}}{36} $
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