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(3x+10)(4x+10)=180
We move all terms to the left:
(3x+10)(4x+10)-(180)=0
We multiply parentheses ..
(+12x^2+30x+40x+100)-180=0
We get rid of parentheses
12x^2+30x+40x+100-180=0
We add all the numbers together, and all the variables
12x^2+70x-80=0
a = 12; b = 70; c = -80;
Δ = b2-4ac
Δ = 702-4·12·(-80)
Δ = 8740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8740}=\sqrt{4*2185}=\sqrt{4}*\sqrt{2185}=2\sqrt{2185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{2185}}{2*12}=\frac{-70-2\sqrt{2185}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{2185}}{2*12}=\frac{-70+2\sqrt{2185}}{24} $
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