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(2x+3)(5x+17)=180
We move all terms to the left:
(2x+3)(5x+17)-(180)=0
We multiply parentheses ..
(+10x^2+34x+15x+51)-180=0
We get rid of parentheses
10x^2+34x+15x+51-180=0
We add all the numbers together, and all the variables
10x^2+49x-129=0
a = 10; b = 49; c = -129;
Δ = b2-4ac
Δ = 492-4·10·(-129)
Δ = 7561
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{-(49)-\sqrt{7561}}{2*10}=\frac{-49-\sqrt{7561}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{7561}}{2*10}=\frac{-49+\sqrt{7561}}{20} $
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