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(2x+5)(x+22)=180
We move all terms to the left:
(2x+5)(x+22)-(180)=0
We multiply parentheses ..
(+2x^2+44x+5x+110)-180=0
We get rid of parentheses
2x^2+44x+5x+110-180=0
We add all the numbers together, and all the variables
2x^2+49x-70=0
a = 2; b = 49; c = -70;
Δ = b2-4ac
Δ = 492-4·2·(-70)
Δ = 2961
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-3\sqrt{329}}{2*2}=\frac{-49-3\sqrt{329}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+3\sqrt{329}}{2*2}=\frac{-49+3\sqrt{329}}{4} $
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