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(2x+15)(5+6x)=180
We move all terms to the left:
(2x+15)(5+6x)-(180)=0
We add all the numbers together, and all the variables
(2x+15)(6x+5)-180=0
We multiply parentheses ..
(+12x^2+10x+90x+75)-180=0
We get rid of parentheses
12x^2+10x+90x+75-180=0
We add all the numbers together, and all the variables
12x^2+100x-105=0
a = 12; b = 100; c = -105;
Δ = b2-4ac
Δ = 1002-4·12·(-105)
Δ = 15040
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15040}=\sqrt{64*235}=\sqrt{64}*\sqrt{235}=8\sqrt{235}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-8\sqrt{235}}{2*12}=\frac{-100-8\sqrt{235}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+8\sqrt{235}}{2*12}=\frac{-100+8\sqrt{235}}{24} $
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