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(5x+6)(9x+7)=0
We multiply parentheses ..
(+45x^2+35x+54x+42)=0
We get rid of parentheses
45x^2+35x+54x+42=0
We add all the numbers together, and all the variables
45x^2+89x+42=0
a = 45; b = 89; c = +42;
Δ = b2-4ac
Δ = 892-4·45·42
Δ = 361
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(89)-19}{2*45}=\frac{-108}{90} =-1+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89)+19}{2*45}=\frac{-70}{90} =-7/9 $
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