7a^2+10a-140=0

Solution for 7a^2+10a-140=0 equation:

7a^2+10a-140=0

a = 7; b = 10; c = -140;
Δ = b2-4ac
Δ = 102-4·7·(-140)
Δ = 4020
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4020}=\sqrt{4*1005}=\sqrt{4}*\sqrt{1005}=2\sqrt{1005}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{1005}}{2*7}=\frac{-10-2\sqrt{1005}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{1005}}{2*7}=\frac{-10+2\sqrt{1005}}{14}
$