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(5x+6)(7x-10)=90
We move all terms to the left:
(5x+6)(7x-10)-(90)=0
We multiply parentheses ..
(+35x^2-50x+42x-60)-90=0
We get rid of parentheses
35x^2-50x+42x-60-90=0
We add all the numbers together, and all the variables
35x^2-8x-150=0
a = 35; b = -8; c = -150;
Δ = b2-4ac
Δ = -82-4·35·(-150)
Δ = 21064
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21064}=\sqrt{4*5266}=\sqrt{4}*\sqrt{5266}=2\sqrt{5266}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{5266}}{2*35}=\frac{8-2\sqrt{5266}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{5266}}{2*35}=\frac{8+2\sqrt{5266}}{70} $
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