(5x-1)+(10x^2+7x)=0

Solution for (5x-1)+(10x^2+7x)=0 equation:

(5x-1)+(10x^2+7x)=0

We get rid of parentheses

10x^2+5x+7x-1=0

We add all the numbers together, and all the variables

10x^2+12x-1=0

a = 10; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·10·(-1)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{46}}{2*10}=\frac{-12-2\sqrt{46}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{46}}{2*10}=\frac{-12+2\sqrt{46}}{20}
$