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(5x+19)(5x+1)+90=180
We move all terms to the left:
(5x+19)(5x+1)+90-(180)=0
We add all the numbers together, and all the variables
(5x+19)(5x+1)-90=0
We multiply parentheses ..
(+25x^2+5x+95x+19)-90=0
We get rid of parentheses
25x^2+5x+95x+19-90=0
We add all the numbers together, and all the variables
25x^2+100x-71=0
a = 25; b = 100; c = -71;
Δ = b2-4ac
Δ = 1002-4·25·(-71)
Δ = 17100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17100}=\sqrt{900*19}=\sqrt{900}*\sqrt{19}=30\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-30\sqrt{19}}{2*25}=\frac{-100-30\sqrt{19}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+30\sqrt{19}}{2*25}=\frac{-100+30\sqrt{19}}{50} $
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