x(2x+7)=270

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Solution for x(2x+7)=270 equation:



x(2x+7)=270
We move all terms to the left:
x(2x+7)-(270)=0
We multiply parentheses
2x^2+7x-270=0
a = 2; b = 7; c = -270;
Δ = b2-4ac
Δ = 72-4·2·(-270)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-47}{2*2}=\frac{-54}{4} =-13+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+47}{2*2}=\frac{40}{4} =10 $

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