(8a+11)(2a+14)+(7a+9)(8a+11)=0

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Solution for (8a+11)(2a+14)+(7a+9)(8a+11)=0 equation:



(8a+11)(2a+14)+(7a+9)(8a+11)=0
We multiply parentheses ..
(+16a^2+112a+22a+154)+(7a+9)(8a+11)=0
We get rid of parentheses
16a^2+112a+22a+(7a+9)(8a+11)+154=0
We multiply parentheses ..
16a^2+(+56a^2+77a+72a+99)+112a+22a+154=0
We add all the numbers together, and all the variables
16a^2+(+56a^2+77a+72a+99)+134a+154=0
We get rid of parentheses
16a^2+56a^2+77a+72a+134a+99+154=0
We add all the numbers together, and all the variables
72a^2+283a+253=0
a = 72; b = 283; c = +253;
Δ = b2-4ac
Δ = 2832-4·72·253
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(283)-85}{2*72}=\frac{-368}{144} =-2+5/9 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(283)+85}{2*72}=\frac{-198}{144} =-1+3/8 $

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