(6x+8)(3x+10)=180

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Solution for (6x+8)(3x+10)=180 equation:



(6x+8)(3x+10)=180
We move all terms to the left:
(6x+8)(3x+10)-(180)=0
We multiply parentheses ..
(+18x^2+60x+24x+80)-180=0
We get rid of parentheses
18x^2+60x+24x+80-180=0
We add all the numbers together, and all the variables
18x^2+84x-100=0
a = 18; b = 84; c = -100;
Δ = b2-4ac
Δ = 842-4·18·(-100)
Δ = 14256
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:
$\sqrt{\Delta}=\sqrt{14256}=\sqrt{1296*11}=\sqrt{1296}*\sqrt{11}=36\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-36\sqrt{11}}{2*18}=\frac{-84-36\sqrt{11}}{36} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+36\sqrt{11}}{2*18}=\frac{-84+36\sqrt{11}}{36} $

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