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(2x+9)(7x+24)=180
We move all terms to the left:
(2x+9)(7x+24)-(180)=0
We multiply parentheses ..
(+14x^2+48x+63x+216)-180=0
We get rid of parentheses
14x^2+48x+63x+216-180=0
We add all the numbers together, and all the variables
14x^2+111x+36=0
a = 14; b = 111; c = +36;
Δ = b2-4ac
Δ = 1112-4·14·36
Δ = 10305
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10305}=\sqrt{9*1145}=\sqrt{9}*\sqrt{1145}=3\sqrt{1145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-3\sqrt{1145}}{2*14}=\frac{-111-3\sqrt{1145}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+3\sqrt{1145}}{2*14}=\frac{-111+3\sqrt{1145}}{28} $
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