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45x^2+6x+-7=(15x+7)
We move all terms to the left:
45x^2+6x+-7-((15x+7))=0
We add all the numbers together, and all the variables
45x^2+6x-((15x+7))=0
We calculate terms in parentheses: -((15x+7)), so:We get rid of parentheses
(15x+7)
We get rid of parentheses
15x+7
Back to the equation:
-(15x+7)
45x^2+6x-15x-7=0
We add all the numbers together, and all the variables
45x^2-9x-7=0
a = 45; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·45·(-7)
Δ = 1341
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1341}=\sqrt{9*149}=\sqrt{9}*\sqrt{149}=3\sqrt{149}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{149}}{2*45}=\frac{9-3\sqrt{149}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{149}}{2*45}=\frac{9+3\sqrt{149}}{90} $
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