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(2x+17)(2x+42)=95
We move all terms to the left:
(2x+17)(2x+42)-(95)=0
We multiply parentheses ..
(+4x^2+84x+34x+714)-95=0
We get rid of parentheses
4x^2+84x+34x+714-95=0
We add all the numbers together, and all the variables
4x^2+118x+619=0
a = 4; b = 118; c = +619;
Δ = b2-4ac
Δ = 1182-4·4·619
Δ = 4020
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4020}=\sqrt{4*1005}=\sqrt{4}*\sqrt{1005}=2\sqrt{1005}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-2\sqrt{1005}}{2*4}=\frac{-118-2\sqrt{1005}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+2\sqrt{1005}}{2*4}=\frac{-118+2\sqrt{1005}}{8} $
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