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(2x+5)(3x-11)=7
We move all terms to the left:
(2x+5)(3x-11)-(7)=0
We multiply parentheses ..
(+6x^2-22x+15x-55)-7=0
We get rid of parentheses
6x^2-22x+15x-55-7=0
We add all the numbers together, and all the variables
6x^2-7x-62=0
a = 6; b = -7; c = -62;
Δ = b2-4ac
Δ = -72-4·6·(-62)
Δ = 1537
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1537}}{2*6}=\frac{7-\sqrt{1537}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1537}}{2*6}=\frac{7+\sqrt{1537}}{12} $
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