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(6x-9)(5x+10)=180
We move all terms to the left:
(6x-9)(5x+10)-(180)=0
We multiply parentheses ..
(+30x^2+60x-45x-90)-180=0
We get rid of parentheses
30x^2+60x-45x-90-180=0
We add all the numbers together, and all the variables
30x^2+15x-270=0
a = 30; b = 15; c = -270;
Δ = b2-4ac
Δ = 152-4·30·(-270)
Δ = 32625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32625}=\sqrt{225*145}=\sqrt{225}*\sqrt{145}=15\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15\sqrt{145}}{2*30}=\frac{-15-15\sqrt{145}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15\sqrt{145}}{2*30}=\frac{-15+15\sqrt{145}}{60} $
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