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7x(2x+5)=4x-9-x
We move all terms to the left:
7x(2x+5)-(4x-9-x)=0
We add all the numbers together, and all the variables
7x(2x+5)-(3x-9)=0
We multiply parentheses
14x^2+35x-(3x-9)=0
We get rid of parentheses
14x^2+35x-3x+9=0
We add all the numbers together, and all the variables
14x^2+32x+9=0
a = 14; b = 32; c = +9;
Δ = b2-4ac
Δ = 322-4·14·9
Δ = 520
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{130}}{2*14}=\frac{-32-2\sqrt{130}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{130}}{2*14}=\frac{-32+2\sqrt{130}}{28} $
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