10x(x+7)+8=148

Solution for 10x(x+7)+8=148 equation:

10x(x+7)+8=148

We move all terms to the left:

10x(x+7)+8-(148)=0

We add all the numbers together, and all the variables

10x(x+7)-140=0

We multiply parentheses

10x^2+70x-140=0

a = 10; b = 70; c = -140;
Δ = b2-4ac
Δ = 702-4·10·(-140)
Δ = 10500
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:

$\sqrt{\Delta}=\sqrt{10500}=\sqrt{100*105}=\sqrt{100}*\sqrt{105}=10\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{105}}{2*10}=\frac{-70-10\sqrt{105}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{105}}{2*10}=\frac{-70+10\sqrt{105}}{20}
$