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(3x+52)(5x+6)=180
We move all terms to the left:
(3x+52)(5x+6)-(180)=0
We multiply parentheses ..
(+15x^2+18x+260x+312)-180=0
We get rid of parentheses
15x^2+18x+260x+312-180=0
We add all the numbers together, and all the variables
15x^2+278x+132=0
a = 15; b = 278; c = +132;
Δ = b2-4ac
Δ = 2782-4·15·132
Δ = 69364
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{69364}=\sqrt{4*17341}=\sqrt{4}*\sqrt{17341}=2\sqrt{17341}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(278)-2\sqrt{17341}}{2*15}=\frac{-278-2\sqrt{17341}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(278)+2\sqrt{17341}}{2*15}=\frac{-278+2\sqrt{17341}}{30} $
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