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(13x+15)(6x+32)=180
We move all terms to the left:
(13x+15)(6x+32)-(180)=0
We multiply parentheses ..
(+78x^2+416x+90x+480)-180=0
We get rid of parentheses
78x^2+416x+90x+480-180=0
We add all the numbers together, and all the variables
78x^2+506x+300=0
a = 78; b = 506; c = +300;
Δ = b2-4ac
Δ = 5062-4·78·300
Δ = 162436
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{162436}=\sqrt{4*40609}=\sqrt{4}*\sqrt{40609}=2\sqrt{40609}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(506)-2\sqrt{40609}}{2*78}=\frac{-506-2\sqrt{40609}}{156} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(506)+2\sqrt{40609}}{2*78}=\frac{-506+2\sqrt{40609}}{156} $
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