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(2x+10)(2x+10)=69
We move all terms to the left:
(2x+10)(2x+10)-(69)=0
We multiply parentheses ..
(+4x^2+20x+20x+100)-69=0
We get rid of parentheses
4x^2+20x+20x+100-69=0
We add all the numbers together, and all the variables
4x^2+40x+31=0
a = 4; b = 40; c = +31;
Δ = b2-4ac
Δ = 402-4·4·31
Δ = 1104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{69}}{2*4}=\frac{-40-4\sqrt{69}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{69}}{2*4}=\frac{-40+4\sqrt{69}}{8} $
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