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2x(3x+5)+90=180
We move all terms to the left:
2x(3x+5)+90-(180)=0
We add all the numbers together, and all the variables
2x(3x+5)-90=0
We multiply parentheses
6x^2+10x-90=0
a = 6; b = 10; c = -90;
Δ = b2-4ac
Δ = 102-4·6·(-90)
Δ = 2260
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{565}}{2*6}=\frac{-10-2\sqrt{565}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{565}}{2*6}=\frac{-10+2\sqrt{565}}{12} $
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