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(5x+7)(3x-1)=4x-5
We move all terms to the left:
(5x+7)(3x-1)-(4x-5)=0
We get rid of parentheses
(5x+7)(3x-1)-4x+5=0
We multiply parentheses ..
(+15x^2-5x+21x-7)-4x+5=0
We get rid of parentheses
15x^2-5x+21x-4x-7+5=0
We add all the numbers together, and all the variables
15x^2+12x-2=0
a = 15; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·15·(-2)
Δ = 264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*15}=\frac{-12-2\sqrt{66}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*15}=\frac{-12+2\sqrt{66}}{30} $
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